diff --git a/src/base/alias.rs b/src/base/alias.rs
index 42cd37a6..fdfda45a 100644
--- a/src/base/alias.rs
+++ b/src/base/alias.rs
@@ -4,8 +4,7 @@ use crate::base::dimension::{U1, U2, U3, U4, U5, U6};
 use crate::base::storage::Owned;
 #[cfg(any(feature = "std", feature = "alloc"))]
 use crate::base::vec_storage::VecStorage;
-use crate::base::Matrix;
-use crate::base::Unit;
+use crate::base::{Const, Matrix, Unit};
 
 /*
  *
@@ -24,11 +23,14 @@ pub type MatrixNM<N, R, C> = Matrix<N, R, C, Owned<N, R, C>>;
 ///
 /// **Because this is an alias, not all its methods are listed here. See the [`Matrix`](crate::base::Matrix) type too.**
 pub type MatrixMN<N, R, C> = Matrix<N, R, C, Owned<N, R, C>>;
+pub type CMatrixMN<N, const R: usize, const C: usize> =
+    Matrix<N, Const<R>, Const<C>, Owned<N, Const<R>, Const<C>>>;
 
 /// A statically sized column-major square matrix with `D` rows and columns.
 ///
 /// **Because this is an alias, not all its methods are listed here. See the [`Matrix`](crate::base::Matrix) type too.**
 pub type MatrixN<N, D> = Matrix<N, D, D, Owned<N, D, D>>;
+pub type CMatrixN<N, const D: usize> = Matrix<N, Const<D>, Const<D>, Owned<N, Const<D>, Const<D>>>;
 
 /// A dynamically sized column-major matrix.
 ///
@@ -266,6 +268,7 @@ pub type DVector<N> = Matrix<N, Dynamic, U1, VecStorage<N, Dynamic, U1>>;
 
 /// A statically sized D-dimensional column vector.
 pub type VectorN<N, D> = Matrix<N, D, U1, Owned<N, D, U1>>;
+pub type CVectorN<N, const D: usize> = Matrix<N, Const<D>, U1, Owned<N, Const<D>, U1>>;
 
 /// A stack-allocated, 1-dimensional column vector.
 pub type Vector1<N> = Matrix<N, U1, U1, Owned<N, U1, U1>>;
diff --git a/src/base/cg.rs b/src/base/cg.rs
index f63cca64..8ffec5cf 100644
--- a/src/base/cg.rs
+++ b/src/base/cg.rs
@@ -416,8 +416,8 @@ where
     #[inline]
     pub fn transform_point(
         &self,
-        pt: &Point<N, DimNameDiff<D, U1>>,
-    ) -> Point<N, DimNameDiff<D, U1>> {
+        pt: &Point<N, { DimNameDiff::<D, U1>::USIZE }>,
+    ) -> Point<N, { DimNameDiff::<D, U1>::USIZE }> {
         let transform = self.fixed_slice::<DimNameDiff<D, U1>, DimNameDiff<D, U1>>(0, 0);
         let translation = self.fixed_slice::<DimNameDiff<D, U1>, U1>(0, D::dim() - 1);
         let normalizer = self.fixed_slice::<U1, DimNameDiff<D, U1>>(D::dim() - 1, 0);
diff --git a/src/base/dimension.rs b/src/base/dimension.rs
index ecc709fb..90a5bdd9 100644
--- a/src/base/dimension.rs
+++ b/src/base/dimension.rs
@@ -201,6 +201,8 @@ pub struct Const<const R: usize>;
 
 /// Trait implemented exclusively by type-level integers.
 pub trait DimName: Dim {
+    const USIZE: usize;
+
     /// The name of this dimension, i.e., the singleton `Self`.
     fn name() -> Self;
 
@@ -233,6 +235,8 @@ impl<const T: usize> Dim for Const<T> {
 }
 
 impl<const T: usize> DimName for Const<T> {
+    const USIZE: usize = T;
+
     #[inline]
     fn name() -> Self {
         Self
diff --git a/src/geometry/abstract_rotation.rs b/src/geometry/abstract_rotation.rs
index 52471851..2c44e46d 100644
--- a/src/geometry/abstract_rotation.rs
+++ b/src/geometry/abstract_rotation.rs
@@ -1,11 +1,10 @@
-use crate::allocator::Allocator;
 use crate::geometry::{Rotation, UnitComplex, UnitQuaternion};
-use crate::{DefaultAllocator, DimName, Point, Scalar, SimdRealField, Unit, VectorN, U2, U3};
+use crate::{CVectorN, Const, Point, Scalar, SimdRealField, Unit, VectorN};
 
 use simba::scalar::ClosedMul;
 
 /// Trait implemented by rotations that can be used inside of an `Isometry` or `Similarity`.
-pub trait AbstractRotation<N: Scalar, D: DimName>: PartialEq + ClosedMul + Clone {
+pub trait AbstractRotation<N: Scalar, const D: usize>: PartialEq + ClosedMul + Clone {
     /// The rotation identity.
     fn identity() -> Self;
     /// The rotation inverse.
@@ -13,34 +12,34 @@ pub trait AbstractRotation<N: Scalar, D: DimName>: PartialEq + ClosedMul + Clone
     /// Change `self` to its inverse.
     fn inverse_mut(&mut self);
     /// Apply the rotation to the given vector.
-    fn transform_vector(&self, v: &VectorN<N, D>) -> VectorN<N, D>
-    where
-        DefaultAllocator: Allocator<N, D>;
+    fn transform_vector(&self, v: &CVectorN<N, D>) -> CVectorN<N, D>;
+    // where
+    //     DefaultAllocator: Allocator<N, D>;
     /// Apply the rotation to the given point.
-    fn transform_point(&self, p: &Point<N, D>) -> Point<N, D>
-    where
-        DefaultAllocator: Allocator<N, D>;
+    fn transform_point(&self, p: &Point<N, D>) -> Point<N, D>;
+    // where
+    //     DefaultAllocator: Allocator<N, D>;
     /// Apply the inverse rotation to the given vector.
-    fn inverse_transform_vector(&self, v: &VectorN<N, D>) -> VectorN<N, D>
-    where
-        DefaultAllocator: Allocator<N, D>;
+    fn inverse_transform_vector(&self, v: &VectorN<N, Const<D>>) -> VectorN<N, Const<D>>;
+    // where
+    //     DefaultAllocator: Allocator<N, D>;
     /// Apply the inverse rotation to the given unit vector.
-    fn inverse_transform_unit_vector(&self, v: &Unit<VectorN<N, D>>) -> Unit<VectorN<N, D>>
-    where
-        DefaultAllocator: Allocator<N, D>,
+    fn inverse_transform_unit_vector(&self, v: &Unit<CVectorN<N, D>>) -> Unit<CVectorN<N, D>>
+// where
+    //     DefaultAllocator: Allocator<N, D>,
     {
         Unit::new_unchecked(self.inverse_transform_vector(&**v))
     }
     /// Apply the inverse rotation to the given point.
-    fn inverse_transform_point(&self, p: &Point<N, D>) -> Point<N, D>
-    where
-        DefaultAllocator: Allocator<N, D>;
+    fn inverse_transform_point(&self, p: &Point<N, D>) -> Point<N, D>;
+    // where
+    //     DefaultAllocator: Allocator<N, D>;
 }
 
-impl<N: SimdRealField, D: DimName> AbstractRotation<N, D> for Rotation<N, D>
+impl<N: SimdRealField, const D: usize> AbstractRotation<N, D> for Rotation<N, D>
 where
     N::Element: SimdRealField,
-    DefaultAllocator: Allocator<N, D, D>,
+    // DefaultAllocator: Allocator<N, D, D>,
 {
     #[inline]
     fn identity() -> Self {
@@ -58,47 +57,47 @@ where
     }
 
     #[inline]
-    fn transform_vector(&self, v: &VectorN<N, D>) -> VectorN<N, D>
-    where
-        DefaultAllocator: Allocator<N, D>,
+    fn transform_vector(&self, v: &CVectorN<N, D>) -> CVectorN<N, D>
+// where
+    //     DefaultAllocator: Allocator<N, D>,
     {
         self * v
     }
 
     #[inline]
     fn transform_point(&self, p: &Point<N, D>) -> Point<N, D>
-    where
-        DefaultAllocator: Allocator<N, D>,
+// where
+    //     DefaultAllocator: Allocator<N, D>,
     {
         self * p
     }
 
     #[inline]
-    fn inverse_transform_vector(&self, v: &VectorN<N, D>) -> VectorN<N, D>
-    where
-        DefaultAllocator: Allocator<N, D>,
+    fn inverse_transform_vector(&self, v: &CVectorN<N, D>) -> CVectorN<N, D>
+// where
+    //     DefaultAllocator: Allocator<N, D>,
     {
         self.inverse_transform_vector(v)
     }
 
     #[inline]
-    fn inverse_transform_unit_vector(&self, v: &Unit<VectorN<N, D>>) -> Unit<VectorN<N, D>>
-    where
-        DefaultAllocator: Allocator<N, D>,
+    fn inverse_transform_unit_vector(&self, v: &Unit<CVectorN<N, D>>) -> Unit<CVectorN<N, D>>
+// where
+    //     DefaultAllocator: Allocator<N, D>,
     {
         self.inverse_transform_unit_vector(v)
     }
 
     #[inline]
     fn inverse_transform_point(&self, p: &Point<N, D>) -> Point<N, D>
-    where
-        DefaultAllocator: Allocator<N, D>,
+// where
+    //     DefaultAllocator: Allocator<N, D>,
     {
         self.inverse_transform_point(p)
     }
 }
 
-impl<N: SimdRealField> AbstractRotation<N, U3> for UnitQuaternion<N>
+impl<N: SimdRealField> AbstractRotation<N, 3> for UnitQuaternion<N>
 where
     N::Element: SimdRealField,
 {
@@ -118,27 +117,27 @@ where
     }
 
     #[inline]
-    fn transform_vector(&self, v: &VectorN<N, U3>) -> VectorN<N, U3> {
+    fn transform_vector(&self, v: &CVectorN<N, 3>) -> CVectorN<N, 3> {
         self * v
     }
 
     #[inline]
-    fn transform_point(&self, p: &Point<N, U3>) -> Point<N, U3> {
+    fn transform_point(&self, p: &Point<N, 3>) -> Point<N, 3> {
         self * p
     }
 
     #[inline]
-    fn inverse_transform_vector(&self, v: &VectorN<N, U3>) -> VectorN<N, U3> {
+    fn inverse_transform_vector(&self, v: &CVectorN<N, 3>) -> CVectorN<N, 3> {
         self.inverse_transform_vector(v)
     }
 
     #[inline]
-    fn inverse_transform_point(&self, p: &Point<N, U3>) -> Point<N, U3> {
+    fn inverse_transform_point(&self, p: &Point<N, 3>) -> Point<N, 3> {
         self.inverse_transform_point(p)
     }
 }
 
-impl<N: SimdRealField> AbstractRotation<N, U2> for UnitComplex<N>
+impl<N: SimdRealField> AbstractRotation<N, 2> for UnitComplex<N>
 where
     N::Element: SimdRealField,
 {
@@ -158,22 +157,22 @@ where
     }
 
     #[inline]
-    fn transform_vector(&self, v: &VectorN<N, U2>) -> VectorN<N, U2> {
+    fn transform_vector(&self, v: &CVectorN<N, 2>) -> CVectorN<N, 2> {
         self * v
     }
 
     #[inline]
-    fn transform_point(&self, p: &Point<N, U2>) -> Point<N, U2> {
+    fn transform_point(&self, p: &Point<N, 2>) -> Point<N, 2> {
         self * p
     }
 
     #[inline]
-    fn inverse_transform_vector(&self, v: &VectorN<N, U2>) -> VectorN<N, U2> {
+    fn inverse_transform_vector(&self, v: &CVectorN<N, 2>) -> CVectorN<N, 2> {
         self.inverse_transform_vector(v)
     }
 
     #[inline]
-    fn inverse_transform_point(&self, p: &Point<N, U2>) -> Point<N, U2> {
+    fn inverse_transform_point(&self, p: &Point<N, 2>) -> Point<N, 2> {
         self.inverse_transform_point(p)
     }
 }
diff --git a/src/geometry/dual_quaternion_conversion.rs b/src/geometry/dual_quaternion_conversion.rs
index 20c6895a..26f3592e 100644
--- a/src/geometry/dual_quaternion_conversion.rs
+++ b/src/geometry/dual_quaternion_conversion.rs
@@ -1,7 +1,6 @@
 use simba::scalar::{RealField, SubsetOf, SupersetOf};
 use simba::simd::SimdRealField;
 
-use crate::base::dimension::U3;
 use crate::base::{Matrix4, Vector4};
 use crate::geometry::{
     DualQuaternion, Isometry3, Similarity3, SuperTCategoryOf, TAffine, Transform, Translation3,
@@ -14,9 +13,9 @@ use crate::geometry::{
  *
  * DualQuaternion     -> DualQuaternion
  * UnitDualQuaternion -> UnitDualQuaternion
- * UnitDualQuaternion -> Isometry<U3>
- * UnitDualQuaternion -> Similarity<U3>
- * UnitDualQuaternion -> Transform<U3>
+ * UnitDualQuaternion -> Isometry<3>
+ * UnitDualQuaternion -> Similarity<3>
+ * UnitDualQuaternion -> Transform<3>
  * UnitDualQuaternion -> Matrix<U4> (homogeneous)
  *
  * NOTE:
@@ -115,24 +114,24 @@ where
     }
 }
 
-impl<N1, N2, C> SubsetOf<Transform<N2, U3, C>> for UnitDualQuaternion<N1>
+impl<N1, N2, C> SubsetOf<Transform<N2, C, 3>> for UnitDualQuaternion<N1>
 where
     N1: RealField,
     N2: RealField + SupersetOf<N1>,
     C: SuperTCategoryOf<TAffine>,
 {
     #[inline]
-    fn to_superset(&self) -> Transform<N2, U3, C> {
+    fn to_superset(&self) -> Transform<N2, C, 3> {
         Transform::from_matrix_unchecked(self.to_homogeneous().to_superset())
     }
 
     #[inline]
-    fn is_in_subset(t: &Transform<N2, U3, C>) -> bool {
+    fn is_in_subset(t: &Transform<N2, C, 3>) -> bool {
         <Self as SubsetOf<_>>::is_in_subset(t.matrix())
     }
 
     #[inline]
-    fn from_superset_unchecked(t: &Transform<N2, U3, C>) -> Self {
+    fn from_superset_unchecked(t: &Transform<N2, C, 3>) -> Self {
         Self::from_superset_unchecked(t.matrix())
     }
 }
diff --git a/src/geometry/isometry.rs b/src/geometry/isometry.rs
index 7e4b703d..144f86b9 100755
--- a/src/geometry/isometry.rs
+++ b/src/geometry/isometry.rs
@@ -14,9 +14,9 @@ use simba::scalar::{RealField, SubsetOf};
 use simba::simd::SimdRealField;
 
 use crate::base::allocator::Allocator;
-use crate::base::dimension::{DimName, DimNameAdd, DimNameSum, U1};
+use crate::base::dimension::{DimNameAdd, DimNameSum, U1};
 use crate::base::storage::Owned;
-use crate::base::{DefaultAllocator, MatrixN, Scalar, Unit, VectorN};
+use crate::base::{CVectorN, Const, DefaultAllocator, MatrixN, Scalar, Unit};
 use crate::geometry::{AbstractRotation, Point, Translation};
 
 /// A direct isometry, i.e., a rotation followed by a translation (aka. a rigid-body motion).
@@ -68,9 +68,9 @@ use crate::geometry::{AbstractRotation, Point, Translation};
                        DefaultAllocator: Allocator<N, D>,
                        Owned<N, D>: Deserialize<'de>"))
 )]
-pub struct Isometry<N: Scalar, D: DimName, R>
-where
-    DefaultAllocator: Allocator<N, D>,
+pub struct Isometry<N: Scalar, R, const D: usize>
+// where
+//     DefaultAllocator: Allocator<N, D>,
 {
     /// The pure rotational part of this isometry.
     pub rotation: R,
@@ -79,13 +79,12 @@ where
 }
 
 #[cfg(feature = "abomonation-serialize")]
-impl<N, D, R> Abomonation for Isometry<N, D, R>
+impl<N, R, const D: usize> Abomonation for Isometry<N, R, D>
 where
     N: SimdRealField,
-    D: DimName,
     R: Abomonation,
     Translation<N, D>: Abomonation,
-    DefaultAllocator: Allocator<N, D>,
+    // DefaultAllocator: Allocator<N, D>,
 {
     unsafe fn entomb<W: Write>(&self, writer: &mut W) -> IOResult<()> {
         self.rotation.entomb(writer)?;
@@ -103,11 +102,10 @@ where
     }
 }
 
-impl<N: Scalar + hash::Hash, D: DimName + hash::Hash, R: hash::Hash> hash::Hash
-    for Isometry<N, D, R>
+impl<N: Scalar + hash::Hash, R: hash::Hash, const D: usize> hash::Hash for Isometry<N, R, D>
 where
-    DefaultAllocator: Allocator<N, D>,
-    Owned<N, D>: hash::Hash,
+    // DefaultAllocator: Allocator<N, D>,
+    Owned<N, Const<D>>: hash::Hash,
 {
     fn hash<H: hash::Hasher>(&self, state: &mut H) {
         self.translation.hash(state);
@@ -115,16 +113,15 @@ where
     }
 }
 
-impl<N: Scalar + Copy, D: DimName + Copy, R: Copy> Copy for Isometry<N, D, R>
-where
-    DefaultAllocator: Allocator<N, D>,
-    Owned<N, D>: Copy,
+impl<N: Scalar + Copy, R: Copy, const D: usize> Copy for Isometry<N, R, D> where
+    // DefaultAllocator: Allocator<N, D>,
+    Owned<N, Const<D>>: Copy
 {
 }
 
-impl<N: Scalar, D: DimName, R: Clone> Clone for Isometry<N, D, R>
-where
-    DefaultAllocator: Allocator<N, D>,
+impl<N: Scalar, R: Clone, const D: usize> Clone for Isometry<N, R, D>
+// where
+//     DefaultAllocator: Allocator<N, D>,
 {
     #[inline]
     fn clone(&self) -> Self {
@@ -135,9 +132,9 @@ where
     }
 }
 /// # From the translation and rotation parts
-impl<N: Scalar, D: DimName, R: AbstractRotation<N, D>> Isometry<N, D, R>
-where
-    DefaultAllocator: Allocator<N, D>,
+impl<N: Scalar, R: AbstractRotation<N, D>, const D: usize> Isometry<N, R, D>
+// where
+//     DefaultAllocator: Allocator<N, D>,
 {
     /// Creates a new isometry from its rotational and translational parts.
     ///
@@ -163,10 +160,10 @@ where
 }
 
 /// # Inversion and in-place composition
-impl<N: SimdRealField, D: DimName, R: AbstractRotation<N, D>> Isometry<N, D, R>
+impl<N: SimdRealField, R: AbstractRotation<N, D>, const D: usize> Isometry<N, R, D>
 where
     N::Element: SimdRealField,
-    DefaultAllocator: Allocator<N, D>,
+    // DefaultAllocator: Allocator<N, D>,
 {
     /// Inverts `self`.
     ///
@@ -223,7 +220,7 @@ where
     /// assert_eq!(iso1.inverse() * iso2, iso1.inv_mul(&iso2));
     /// ```
     #[inline]
-    pub fn inv_mul(&self, rhs: &Isometry<N, D, R>) -> Self {
+    pub fn inv_mul(&self, rhs: &Isometry<N, R, D>) -> Self {
         let inv_rot1 = self.rotation.inverse();
         let tr_12 = rhs.translation.vector.clone() - self.translation.vector.clone();
         Isometry::from_parts(
@@ -318,10 +315,10 @@ where
 }
 
 /// # Transformation of a vector or a point
-impl<N: SimdRealField, D: DimName, R: AbstractRotation<N, D>> Isometry<N, D, R>
+impl<N: SimdRealField, R: AbstractRotation<N, D>, const D: usize> Isometry<N, R, D>
 where
     N::Element: SimdRealField,
-    DefaultAllocator: Allocator<N, D>,
+    // DefaultAllocator: Allocator<N, D>,
 {
     /// Transform the given point by this isometry.
     ///
@@ -364,7 +361,7 @@ where
     /// assert_relative_eq!(transformed_point, Vector3::new(3.0, 2.0, -1.0), epsilon = 1.0e-6);
     /// ```
     #[inline]
-    pub fn transform_vector(&self, v: &VectorN<N, D>) -> VectorN<N, D> {
+    pub fn transform_vector(&self, v: &CVectorN<N, D>) -> CVectorN<N, D> {
         self * v
     }
 
@@ -410,7 +407,7 @@ where
     /// assert_relative_eq!(transformed_point, Vector3::new(-3.0, 2.0, 1.0), epsilon = 1.0e-6);
     /// ```
     #[inline]
-    pub fn inverse_transform_vector(&self, v: &VectorN<N, D>) -> VectorN<N, D> {
+    pub fn inverse_transform_vector(&self, v: &CVectorN<N, D>) -> CVectorN<N, D> {
         self.rotation.inverse_transform_vector(v)
     }
 
@@ -433,7 +430,7 @@ where
     /// assert_relative_eq!(transformed_point, -Vector3::y_axis(), epsilon = 1.0e-6);
     /// ```
     #[inline]
-    pub fn inverse_transform_unit_vector(&self, v: &Unit<VectorN<N, D>>) -> Unit<VectorN<N, D>> {
+    pub fn inverse_transform_unit_vector(&self, v: &Unit<CVectorN<N, D>>) -> Unit<CVectorN<N, D>> {
         self.rotation.inverse_transform_unit_vector(v)
     }
 }
@@ -443,9 +440,9 @@ where
 // This is OK since all constructors of the isometry enforce the Rotation bound already (and
 // explicit struct construction is prevented by the dummy ZST field).
 /// # Conversion to a matrix
-impl<N: SimdRealField, D: DimName, R> Isometry<N, D, R>
-where
-    DefaultAllocator: Allocator<N, D>,
+impl<N: SimdRealField, R, const D: usize> Isometry<N, R, D>
+// where
+//     DefaultAllocator: Allocator<N, D>,
 {
     /// Converts this isometry into its equivalent homogeneous transformation matrix.
     ///
@@ -465,14 +462,14 @@ where
     /// assert_relative_eq!(iso.to_homogeneous(), expected, epsilon = 1.0e-6);
     /// ```
     #[inline]
-    pub fn to_homogeneous(&self) -> MatrixN<N, DimNameSum<D, U1>>
+    pub fn to_homogeneous(&self) -> MatrixN<N, DimNameSum<Const<D>, U1>>
     where
-        D: DimNameAdd<U1>,
-        R: SubsetOf<MatrixN<N, DimNameSum<D, U1>>>,
-        DefaultAllocator: Allocator<N, DimNameSum<D, U1>, DimNameSum<D, U1>>,
+        Const<D>: DimNameAdd<U1>,
+        R: SubsetOf<MatrixN<N, DimNameSum<Const<D>, U1>>>,
+        DefaultAllocator: Allocator<N, DimNameSum<Const<D>, U1>, DimNameSum<Const<D>, U1>>,
     {
         let mut res: MatrixN<N, _> = crate::convert_ref(&self.rotation);
-        res.fixed_slice_mut::<D, U1>(0, D::dim())
+        res.fixed_slice_mut::<Const<D>, U1>(0, D)
             .copy_from(&self.translation.vector);
 
         res
@@ -496,27 +493,25 @@ where
     /// assert_relative_eq!(iso.to_matrix(), expected, epsilon = 1.0e-6);
     /// ```
     #[inline]
-    pub fn to_matrix(&self) -> MatrixN<N, DimNameSum<D, U1>>
+    pub fn to_matrix(&self) -> MatrixN<N, DimNameSum<Const<D>, U1>>
     where
-        D: DimNameAdd<U1>,
-        R: SubsetOf<MatrixN<N, DimNameSum<D, U1>>>,
-        DefaultAllocator: Allocator<N, DimNameSum<D, U1>, DimNameSum<D, U1>>,
+        Const<D>: DimNameAdd<U1>,
+        R: SubsetOf<MatrixN<N, DimNameSum<Const<D>, U1>>>,
+        DefaultAllocator: Allocator<N, DimNameSum<Const<D>, U1>, DimNameSum<Const<D>, U1>>,
     {
         self.to_homogeneous()
     }
 }
 
-impl<N: SimdRealField, D: DimName, R> Eq for Isometry<N, D, R>
-where
-    R: AbstractRotation<N, D> + Eq,
-    DefaultAllocator: Allocator<N, D>,
+impl<N: SimdRealField, R, const D: usize> Eq for Isometry<N, R, D> where
+    R: AbstractRotation<N, D> + Eq // DefaultAllocator: Allocator<N, D>,
 {
 }
 
-impl<N: SimdRealField, D: DimName, R> PartialEq for Isometry<N, D, R>
+impl<N: SimdRealField, R, const D: usize> PartialEq for Isometry<N, R, D>
 where
     R: AbstractRotation<N, D> + PartialEq,
-    DefaultAllocator: Allocator<N, D>,
+    // DefaultAllocator: Allocator<N, D>,
 {
     #[inline]
     fn eq(&self, right: &Self) -> bool {
@@ -524,10 +519,10 @@ where
     }
 }
 
-impl<N: RealField, D: DimName, R> AbsDiffEq for Isometry<N, D, R>
+impl<N: RealField, R, const D: usize> AbsDiffEq for Isometry<N, R, D>
 where
     R: AbstractRotation<N, D> + AbsDiffEq<Epsilon = N::Epsilon>,
-    DefaultAllocator: Allocator<N, D>,
+    // DefaultAllocator: Allocator<N, D>,
     N::Epsilon: Copy,
 {
     type Epsilon = N::Epsilon;
@@ -544,10 +539,10 @@ where
     }
 }
 
-impl<N: RealField, D: DimName, R> RelativeEq for Isometry<N, D, R>
+impl<N: RealField, R, const D: usize> RelativeEq for Isometry<N, R, D>
 where
     R: AbstractRotation<N, D> + RelativeEq<Epsilon = N::Epsilon>,
-    DefaultAllocator: Allocator<N, D>,
+    // DefaultAllocator: Allocator<N, D>,
     N::Epsilon: Copy,
 {
     #[inline]
@@ -570,10 +565,10 @@ where
     }
 }
 
-impl<N: RealField, D: DimName, R> UlpsEq for Isometry<N, D, R>
+impl<N: RealField, R, const D: usize> UlpsEq for Isometry<N, R, D>
 where
     R: AbstractRotation<N, D> + UlpsEq<Epsilon = N::Epsilon>,
-    DefaultAllocator: Allocator<N, D>,
+    // DefaultAllocator: Allocator<N, D>,
     N::Epsilon: Copy,
 {
     #[inline]
@@ -594,10 +589,10 @@ where
  * Display
  *
  */
-impl<N: RealField + fmt::Display, D: DimName, R> fmt::Display for Isometry<N, D, R>
+impl<N: RealField + fmt::Display, R, const D: usize> fmt::Display for Isometry<N, R, D>
 where
     R: fmt::Display,
-    DefaultAllocator: Allocator<N, D> + Allocator<usize, D>,
+    // DefaultAllocator: Allocator<N, D> + Allocator<usize, D>,
 {
     fn fmt(&self, f: &mut fmt::Formatter) -> fmt::Result {
         let precision = f.precision().unwrap_or(3);
diff --git a/src/geometry/isometry_alias.rs b/src/geometry/isometry_alias.rs
index 8eecd3ee..3ac2db56 100644
--- a/src/geometry/isometry_alias.rs
+++ b/src/geometry/isometry_alias.rs
@@ -1,5 +1,3 @@
-use crate::base::dimension::{U2, U3};
-
 use crate::geometry::{Isometry, Rotation2, Rotation3, UnitComplex, UnitQuaternion};
 
 /// A 2-dimensional direct isometry using a unit complex number for its rotational part.
@@ -8,28 +6,28 @@ use crate::geometry::{Isometry, Rotation2, Rotation3, UnitComplex, UnitQuaternio
 ///
 /// Also known as a 2D rigid-body motion, or as an element of SE(2).
 
-pub type Isometry2<N> = Isometry<N, U2, UnitComplex<N>>;
+pub type Isometry2<N> = Isometry<N, UnitComplex<N>, 2>;
 
 /// A 3-dimensional direct isometry using a unit quaternion for its rotational part.
 ///
 /// **Because this is an alias, not all its methods are listed here. See the [`Isometry`](crate::Isometry) type too.**
 ///
 /// Also known as a rigid-body motion, or as an element of SE(3).
-pub type Isometry3<N> = Isometry<N, U3, UnitQuaternion<N>>;
+pub type Isometry3<N> = Isometry<N, UnitQuaternion<N>, 3>;
 
 /// A 2-dimensional direct isometry using a rotation matrix for its rotational part.
 ///
 /// **Because this is an alias, not all its methods are listed here. See the [`Isometry`](crate::Isometry) type too.**
 ///
 /// Also known as a rigid-body motion, or as an element of SE(2).
-pub type IsometryMatrix2<N> = Isometry<N, U2, Rotation2<N>>;
+pub type IsometryMatrix2<N> = Isometry<N, Rotation2<N>, 2>;
 
 /// A 3-dimensional direct isometry using a rotation matrix for its rotational part.
 ///
 /// **Because this is an alias, not all its methods are listed here. See the [`Isometry`](crate::Isometry) type too.**
 ///
 /// Also known as a rigid-body motion, or as an element of SE(3).
-pub type IsometryMatrix3<N> = Isometry<N, U3, Rotation3<N>>;
+pub type IsometryMatrix3<N> = Isometry<N, Rotation3<N>, 3>;
 
 // This tests that the types correctly implement `Copy`, without having to run tests
 // (when targeting no-std for example).
diff --git a/src/geometry/isometry_construction.rs b/src/geometry/isometry_construction.rs
index 1edf269b..7a6b870f 100644
--- a/src/geometry/isometry_construction.rs
+++ b/src/geometry/isometry_construction.rs
@@ -13,9 +13,8 @@ use rand::{
 use simba::scalar::SupersetOf;
 use simba::simd::SimdRealField;
 
-use crate::base::allocator::Allocator;
-use crate::base::dimension::{DimName, U2};
-use crate::base::{DefaultAllocator, Vector2, Vector3};
+use crate::base::dimension::U2;
+use crate::base::{Vector2, Vector3};
 
 use crate::{
     AbstractRotation, Isometry, Isometry2, Isometry3, IsometryMatrix2, IsometryMatrix3, Point,
@@ -23,10 +22,10 @@ use crate::{
     UnitQuaternion,
 };
 
-impl<N: SimdRealField, D: DimName, R: AbstractRotation<N, D>> Isometry<N, D, R>
+impl<N: SimdRealField, R: AbstractRotation<N, D>, const D: usize> Isometry<N, R, D>
 where
     N::Element: SimdRealField,
-    DefaultAllocator: Allocator<N, D>,
+    // DefaultAllocator: Allocator<N, D>,
 {
     /// Creates a new identity isometry.
     ///
@@ -71,10 +70,10 @@ where
     }
 }
 
-impl<N: SimdRealField, D: DimName, R: AbstractRotation<N, D>> One for Isometry<N, D, R>
+impl<N: SimdRealField, R: AbstractRotation<N, D>, const D: usize> One for Isometry<N, R, D>
 where
     N::Element: SimdRealField,
-    DefaultAllocator: Allocator<N, D>,
+    // DefaultAllocator: Allocator<N, D>,
 {
     /// Creates a new identity isometry.
     #[inline]
@@ -84,26 +83,26 @@ where
 }
 
 #[cfg(feature = "rand-no-std")]
-impl<N: crate::RealField, D: DimName, R> Distribution<Isometry<N, D, R>> for Standard
+impl<N: crate::RealField, R, const D: usize> Distribution<Isometry<N, R, D>> for Standard
 where
     R: AbstractRotation<N, D>,
     Standard: Distribution<N> + Distribution<R>,
-    DefaultAllocator: Allocator<N, D>,
+    // DefaultAllocator: Allocator<N, D>,
 {
     #[inline]
-    fn sample<'a, G: Rng + ?Sized>(&self, rng: &'a mut G) -> Isometry<N, D, R> {
+    fn sample<'a, G: Rng + ?Sized>(&self, rng: &'a mut G) -> Isometry<N, R, D> {
         Isometry::from_parts(rng.gen(), rng.gen())
     }
 }
 
 #[cfg(feature = "arbitrary")]
-impl<N, D: DimName, R> Arbitrary for Isometry<N, D, R>
+impl<N, R, const D: usize> Arbitrary for Isometry<N, R, D>
 where
     N: SimdRealField + Arbitrary + Send,
     N::Element: SimdRealField,
     R: AbstractRotation<N, D> + Arbitrary + Send,
     Owned<N, D>: Send,
-    DefaultAllocator: Allocator<N, D>,
+    // DefaultAllocator: Allocator<N, D>,
 {
     #[inline]
     fn arbitrary(rng: &mut Gen) -> Self {
diff --git a/src/geometry/isometry_conversion.rs b/src/geometry/isometry_conversion.rs
index 0c89958a..e75570c2 100644
--- a/src/geometry/isometry_conversion.rs
+++ b/src/geometry/isometry_conversion.rs
@@ -2,8 +2,8 @@ use simba::scalar::{RealField, SubsetOf, SupersetOf};
 use simba::simd::{PrimitiveSimdValue, SimdRealField, SimdValue};
 
 use crate::base::allocator::Allocator;
-use crate::base::dimension::{DimMin, DimName, DimNameAdd, DimNameSum, U1};
-use crate::base::{DefaultAllocator, MatrixN, Scalar};
+use crate::base::dimension::{DimMin, DimNameAdd, DimNameSum, U1};
+use crate::base::{Const, DefaultAllocator, MatrixN, Scalar};
 
 use crate::geometry::{
     AbstractRotation, Isometry, Isometry3, Similarity, SuperTCategoryOf, TAffine, Transform,
@@ -21,27 +21,27 @@ use crate::geometry::{
  * Isometry -> Matrix (homogeneous)
  */
 
-impl<N1, N2, D: DimName, R1, R2> SubsetOf<Isometry<N2, D, R2>> for Isometry<N1, D, R1>
+impl<N1, N2, R1, R2, const D: usize> SubsetOf<Isometry<N2, R2, D>> for Isometry<N1, R1, D>
 where
     N1: RealField,
     N2: RealField + SupersetOf<N1>,
     R1: AbstractRotation<N1, D> + SubsetOf<R2>,
     R2: AbstractRotation<N2, D>,
-    DefaultAllocator: Allocator<N1, D> + Allocator<N2, D>,
+    // DefaultAllocator: Allocator<N1, D> + Allocator<N2, D>,
 {
     #[inline]
-    fn to_superset(&self) -> Isometry<N2, D, R2> {
+    fn to_superset(&self) -> Isometry<N2, R2, D> {
         Isometry::from_parts(self.translation.to_superset(), self.rotation.to_superset())
     }
 
     #[inline]
-    fn is_in_subset(iso: &Isometry<N2, D, R2>) -> bool {
+    fn is_in_subset(iso: &Isometry<N2, R2, D>) -> bool {
         crate::is_convertible::<_, Translation<N1, D>>(&iso.translation)
             && crate::is_convertible::<_, R1>(&iso.rotation)
     }
 
     #[inline]
-    fn from_superset_unchecked(iso: &Isometry<N2, D, R2>) -> Self {
+    fn from_superset_unchecked(iso: &Isometry<N2, R2, D>) -> Self {
         Isometry::from_parts(
             iso.translation.to_subset_unchecked(),
             iso.rotation.to_subset_unchecked(),
@@ -73,102 +73,101 @@ where
     }
 }
 
-impl<N1, N2, D: DimName, R1, R2> SubsetOf<Similarity<N2, D, R2>> for Isometry<N1, D, R1>
+impl<N1, N2, R1, R2, const D: usize> SubsetOf<Similarity<N2, R2, D>> for Isometry<N1, R1, D>
 where
     N1: RealField,
     N2: RealField + SupersetOf<N1>,
     R1: AbstractRotation<N1, D> + SubsetOf<R2>,
     R2: AbstractRotation<N2, D>,
-    DefaultAllocator: Allocator<N1, D> + Allocator<N2, D>,
+    // DefaultAllocator: Allocator<N1, D> + Allocator<N2, D>,
 {
     #[inline]
-    fn to_superset(&self) -> Similarity<N2, D, R2> {
+    fn to_superset(&self) -> Similarity<N2, R2, D> {
         Similarity::from_isometry(self.to_superset(), N2::one())
     }
 
     #[inline]
-    fn is_in_subset(sim: &Similarity<N2, D, R2>) -> bool {
-        crate::is_convertible::<_, Isometry<N1, D, R1>>(&sim.isometry) && sim.scaling() == N2::one()
+    fn is_in_subset(sim: &Similarity<N2, R2, D>) -> bool {
+        crate::is_convertible::<_, Isometry<N1, R1, D>>(&sim.isometry) && sim.scaling() == N2::one()
     }
 
     #[inline]
-    fn from_superset_unchecked(sim: &Similarity<N2, D, R2>) -> Self {
+    fn from_superset_unchecked(sim: &Similarity<N2, R2, D>) -> Self {
         crate::convert_ref_unchecked(&sim.isometry)
     }
 }
 
-impl<N1, N2, D, R, C> SubsetOf<Transform<N2, D, C>> for Isometry<N1, D, R>
+impl<N1, N2, R, C, const D: usize> SubsetOf<Transform<N2, C, D>> for Isometry<N1, R, D>
 where
     N1: RealField,
     N2: RealField + SupersetOf<N1>,
     C: SuperTCategoryOf<TAffine>,
     R: AbstractRotation<N1, D>
-        + SubsetOf<MatrixN<N1, DimNameSum<D, U1>>>
-        + SubsetOf<MatrixN<N2, DimNameSum<D, U1>>>,
-    D: DimNameAdd<U1> + DimMin<D, Output = D>, // needed by .is_special_orthogonal()
-    DefaultAllocator: Allocator<N1, D>
-        + Allocator<N1, D, D>
-        + Allocator<N1, DimNameSum<D, U1>, DimNameSum<D, U1>>
-        + Allocator<N2, DimNameSum<D, U1>, DimNameSum<D, U1>>
-        + Allocator<N2, DimNameSum<D, U1>, DimNameSum<D, U1>>
-        + Allocator<(usize, usize), D>
-        + Allocator<N2, D, D>
-        + Allocator<N2, D>,
+        + SubsetOf<MatrixN<N1, DimNameSum<Const<D>, U1>>>
+        + SubsetOf<MatrixN<N2, DimNameSum<Const<D>, U1>>>,
+    Const<D>: DimNameAdd<U1> + DimMin<Const<D>, Output = Const<D>>, // needed by .is_special_orthogonal()
+    DefaultAllocator: Allocator<N1, DimNameSum<Const<D>, U1>, DimNameSum<Const<D>, U1>>
+        + Allocator<N2, DimNameSum<Const<D>, U1>, DimNameSum<Const<D>, U1>>
+        + Allocator<N2, DimNameSum<Const<D>, U1>, DimNameSum<Const<D>, U1>>,
+    // + Allocator<N1, D>
+    // + Allocator<(usize, usize), D>
+    // + Allocator<N2, D, D>
+    // + Allocator<N2, D>
 {
     #[inline]
-    fn to_superset(&self) -> Transform<N2, D, C> {
+    fn to_superset(&self) -> Transform<N2, C, D> {
         Transform::from_matrix_unchecked(self.to_homogeneous().to_superset())
     }
 
     #[inline]
-    fn is_in_subset(t: &Transform<N2, D, C>) -> bool {
+    fn is_in_subset(t: &Transform<N2, C, D>) -> bool {
         <Self as SubsetOf<_>>::is_in_subset(t.matrix())
     }
 
     #[inline]
-    fn from_superset_unchecked(t: &Transform<N2, D, C>) -> Self {
+    fn from_superset_unchecked(t: &Transform<N2, C, D>) -> Self {
         Self::from_superset_unchecked(t.matrix())
     }
 }
 
-impl<N1, N2, D, R> SubsetOf<MatrixN<N2, DimNameSum<D, U1>>> for Isometry<N1, D, R>
+impl<N1, N2, R, const D: usize> SubsetOf<MatrixN<N2, DimNameSum<Const<D>, U1>>>
+    for Isometry<N1, R, D>
 where
     N1: RealField,
     N2: RealField + SupersetOf<N1>,
     R: AbstractRotation<N1, D>
-        + SubsetOf<MatrixN<N1, DimNameSum<D, U1>>>
-        + SubsetOf<MatrixN<N2, DimNameSum<D, U1>>>,
-    D: DimNameAdd<U1> + DimMin<D, Output = D>, // needed by .is_special_orthogonal()
-    DefaultAllocator: Allocator<N1, D>
-        + Allocator<N1, D, D>
-        + Allocator<N1, DimNameSum<D, U1>, DimNameSum<D, U1>>
-        + Allocator<N2, DimNameSum<D, U1>, DimNameSum<D, U1>>
-        + Allocator<N2, DimNameSum<D, U1>, DimNameSum<D, U1>>
-        + Allocator<(usize, usize), D>
-        + Allocator<N2, D, D>
-        + Allocator<N2, D>,
+        + SubsetOf<MatrixN<N1, DimNameSum<Const<D>, U1>>>
+        + SubsetOf<MatrixN<N2, DimNameSum<Const<D>, U1>>>,
+    Const<D>: DimNameAdd<U1> + DimMin<Const<D>, Output = Const<D>>, // needed by .is_special_orthogonal()
+    DefaultAllocator: Allocator<N1, DimNameSum<Const<D>, U1>, DimNameSum<Const<D>, U1>>
+        + Allocator<N2, DimNameSum<Const<D>, U1>, DimNameSum<Const<D>, U1>>
+        + Allocator<N2, DimNameSum<Const<D>, U1>, DimNameSum<Const<D>, U1>>, // + Allocator<(usize, usize), D>
+                                                                             // + Allocator<N2, D, D>
+                                                                             // + Allocator<N2, D>
+                                                                             // + Allocator<N1, D>
+                                                                             // + Allocator<N1, D, D>
 {
     #[inline]
-    fn to_superset(&self) -> MatrixN<N2, DimNameSum<D, U1>> {
+    fn to_superset(&self) -> MatrixN<N2, DimNameSum<Const<D>, U1>> {
         self.to_homogeneous().to_superset()
     }
 
     #[inline]
-    fn is_in_subset(m: &MatrixN<N2, DimNameSum<D, U1>>) -> bool {
+    fn is_in_subset(m: &MatrixN<N2, DimNameSum<Const<D>, U1>>) -> bool {
         let rot = m.fixed_slice::<D, D>(0, 0);
-        let bottom = m.fixed_slice::<U1, D>(D::dim(), 0);
+        let bottom = m.fixed_slice::<U1, D>(D, 0);
 
         // Scalar types agree.
         m.iter().all(|e| SupersetOf::<N1>::is_in_subset(e)) &&
         // The block part is a rotation.
         rot.is_special_orthogonal(N2::default_epsilon() * crate::convert(100.0)) &&
         // The bottom row is (0, 0, ..., 1)
-        bottom.iter().all(|e| e.is_zero()) && m[(D::dim(), D::dim())] == N2::one()
+        bottom.iter().all(|e| e.is_zero()) && m[(D, D)] == N2::one()
     }
 
     #[inline]
-    fn from_superset_unchecked(m: &MatrixN<N2, DimNameSum<D, U1>>) -> Self {
-        let t = m.fixed_slice::<D, U1>(0, D::dim()).into_owned();
+    fn from_superset_unchecked(m: &MatrixN<N2, DimNameSum<Const<D>, U1>>) -> Self {
+        let t = m.fixed_slice::<D, U1>(0, D).into_owned();
         let t = Translation {
             vector: crate::convert_unchecked(t),
         };
@@ -177,10 +176,10 @@ where
     }
 }
 
-impl<N: SimdRealField, D: DimName, R: AbstractRotation<N, D>> From<Translation<N, D>>
-    for Isometry<N, D, R>
-where
-    DefaultAllocator: Allocator<N, D>,
+impl<N: SimdRealField, R: AbstractRotation<N, D>, const D: usize> From<Translation<N, D>>
+    for Isometry<N, R, D>
+// where
+//     DefaultAllocator: Allocator<N, D>,
 {
     #[inline]
     fn from(tra: Translation<N, D>) -> Self {
@@ -188,30 +187,31 @@ where
     }
 }
 
-impl<N: SimdRealField, D: DimName, R> From<Isometry<N, D, R>> for MatrixN<N, DimNameSum<D, U1>>
+impl<N: SimdRealField, R, const D: usize> From<Isometry<N, R, D>>
+    for MatrixN<N, DimNameSum<Const<D>, U1>>
 where
-    D: DimNameAdd<U1>,
-    R: SubsetOf<MatrixN<N, DimNameSum<D, U1>>>,
-    DefaultAllocator: Allocator<N, DimNameSum<D, U1>, DimNameSum<D, U1>> + Allocator<N, D>,
+    Const<D>: DimNameAdd<U1>,
+    R: SubsetOf<MatrixN<N, DimNameSum<Const<D>, U1>>>,
+    DefaultAllocator: Allocator<N, DimNameSum<Const<D>, U1>, DimNameSum<Const<D>, U1>>, // + Allocator<N, D>,
 {
     #[inline]
-    fn from(iso: Isometry<N, D, R>) -> Self {
+    fn from(iso: Isometry<N, R, D>) -> Self {
         iso.to_homogeneous()
     }
 }
 
-impl<N: Scalar + PrimitiveSimdValue, D: DimName, R> From<[Isometry<N::Element, D, R::Element>; 2]>
-    for Isometry<N, D, R>
+impl<N: Scalar + PrimitiveSimdValue, R, const D: usize>
+    From<[Isometry<N::Element, R::Element, D>; 2]> for Isometry<N, R, D>
 where
     N: From<[<N as SimdValue>::Element; 2]>,
     R: SimdValue + AbstractRotation<N, D> + From<[<R as SimdValue>::Element; 2]>,
     R::Element: AbstractRotation<N::Element, D>,
     N::Element: Scalar + Copy,
     R::Element: Scalar + Copy,
-    DefaultAllocator: Allocator<N, D> + Allocator<N::Element, D>,
+    // DefaultAllocator: Allocator<N, D> + Allocator<N::Element, D>,
 {
     #[inline]
-    fn from(arr: [Isometry<N::Element, D, R::Element>; 2]) -> Self {
+    fn from(arr: [Isometry<N::Element, R::Element, D>; 2]) -> Self {
         let tra = Translation::from([arr[0].translation.clone(), arr[1].translation.clone()]);
         let rot = R::from([arr[0].rotation, arr[0].rotation]);
 
@@ -219,18 +219,18 @@ where
     }
 }
 
-impl<N: Scalar + PrimitiveSimdValue, D: DimName, R> From<[Isometry<N::Element, D, R::Element>; 4]>
-    for Isometry<N, D, R>
+impl<N: Scalar + PrimitiveSimdValue, R, const D: usize>
+    From<[Isometry<N::Element, R::Element, D>; 4]> for Isometry<N, R, D>
 where
     N: From<[<N as SimdValue>::Element; 4]>,
     R: SimdValue + AbstractRotation<N, D> + From<[<R as SimdValue>::Element; 4]>,
     R::Element: AbstractRotation<N::Element, D>,
     N::Element: Scalar + Copy,
     R::Element: Scalar + Copy,
-    DefaultAllocator: Allocator<N, D> + Allocator<N::Element, D>,
+    // DefaultAllocator: Allocator<N, D> + Allocator<N::Element, D>,
 {
     #[inline]
-    fn from(arr: [Isometry<N::Element, D, R::Element>; 4]) -> Self {
+    fn from(arr: [Isometry<N::Element, R::Element, D>; 4]) -> Self {
         let tra = Translation::from([
             arr[0].translation.clone(),
             arr[1].translation.clone(),
@@ -248,18 +248,18 @@ where
     }
 }
 
-impl<N: Scalar + PrimitiveSimdValue, D: DimName, R> From<[Isometry<N::Element, D, R::Element>; 8]>
-    for Isometry<N, D, R>
+impl<N: Scalar + PrimitiveSimdValue, R, const D: usize>
+    From<[Isometry<N::Element, R::Element, D>; 8]> for Isometry<N, R, D>
 where
     N: From<[<N as SimdValue>::Element; 8]>,
     R: SimdValue + AbstractRotation<N, D> + From<[<R as SimdValue>::Element; 8]>,
     R::Element: AbstractRotation<N::Element, D>,
     N::Element: Scalar + Copy,
     R::Element: Scalar + Copy,
-    DefaultAllocator: Allocator<N, D> + Allocator<N::Element, D>,
+    // DefaultAllocator: Allocator<N, D> + Allocator<N::Element, D>,
 {
     #[inline]
-    fn from(arr: [Isometry<N::Element, D, R::Element>; 8]) -> Self {
+    fn from(arr: [Isometry<N::Element, R::Element, D>; 8]) -> Self {
         let tra = Translation::from([
             arr[0].translation.clone(),
             arr[1].translation.clone(),
@@ -285,18 +285,18 @@ where
     }
 }
 
-impl<N: Scalar + PrimitiveSimdValue, D: DimName, R> From<[Isometry<N::Element, D, R::Element>; 16]>
-    for Isometry<N, D, R>
+impl<N: Scalar + PrimitiveSimdValue, R, const D: usize>
+    From<[Isometry<N::Element, R::Element, D>; 16]> for Isometry<N, R, D>
 where
     N: From<[<N as SimdValue>::Element; 16]>,
     R: SimdValue + AbstractRotation<N, D> + From<[<R as SimdValue>::Element; 16]>,
     R::Element: AbstractRotation<N::Element, D>,
     N::Element: Scalar + Copy,
     R::Element: Scalar + Copy,
-    DefaultAllocator: Allocator<N, D> + Allocator<N::Element, D>,
+    // DefaultAllocator: Allocator<N, D> + Allocator<N::Element, D>,
 {
     #[inline]
-    fn from(arr: [Isometry<N::Element, D, R::Element>; 16]) -> Self {
+    fn from(arr: [Isometry<N::Element, R::Element, D>; 16]) -> Self {
         let tra = Translation::from([
             arr[0].translation.clone(),
             arr[1].translation.clone(),
diff --git a/src/geometry/isometry_simba.rs b/src/geometry/isometry_simba.rs
index e5d2c839..1db8dd43 100755
--- a/src/geometry/isometry_simba.rs
+++ b/src/geometry/isometry_simba.rs
@@ -1,20 +1,17 @@
 use simba::simd::SimdValue;
 
-use crate::base::allocator::Allocator;
-use crate::base::dimension::DimName;
-use crate::base::DefaultAllocator;
 use crate::SimdRealField;
 
 use crate::geometry::{AbstractRotation, Isometry, Translation};
 
-impl<N: SimdRealField, D: DimName, R> SimdValue for Isometry<N, D, R>
+impl<N: SimdRealField, R, const D: usize> SimdValue for Isometry<N, R, D>
 where
     N::Element: SimdRealField,
     R: SimdValue<SimdBool = N::SimdBool> + AbstractRotation<N, D>,
     R::Element: AbstractRotation<N::Element, D>,
-    DefaultAllocator: Allocator<N, D> + Allocator<N::Element, D>,
+    // DefaultAllocator: Allocator<N, D> + Allocator<N::Element, D>,
 {
-    type Element = Isometry<N::Element, D, R::Element>;
+    type Element = Isometry<N::Element, R::Element, D>;
     type SimdBool = N::SimdBool;
 
     #[inline]
diff --git a/src/geometry/point.rs b/src/geometry/point.rs
index 5d8b6fbd..307f0b17 100644
--- a/src/geometry/point.rs
+++ b/src/geometry/point.rs
@@ -40,54 +40,49 @@ use crate::base::{Const, DefaultAllocator, Scalar, VectorN};
 /// of said transformations for details.
 #[repr(C)]
 #[derive(Debug, Clone)]
-pub struct Point<N: Scalar, D: DimName>
-where
-    DefaultAllocator: Allocator<N, D>,
-{
+pub struct Point<N: Scalar, const D: usize> {
     /// The coordinates of this point, i.e., the shift from the origin.
-    pub coords: VectorN<N, D>,
+    pub coords: VectorN<N, Const<D>>,
 }
 
-impl<N: Scalar + hash::Hash, D: DimName + hash::Hash> hash::Hash for Point<N, D>
-where
-    DefaultAllocator: Allocator<N, D>,
-    <DefaultAllocator as Allocator<N, D>>::Buffer: hash::Hash,
+impl<N: Scalar + hash::Hash, const D: usize> hash::Hash for Point<N, D>
+// where
+//     DefaultAllocator: Allocator<N, D>,
+//     <DefaultAllocator as Allocator<N, D>>::Buffer: hash::Hash,
 {
     fn hash<H: hash::Hasher>(&self, state: &mut H) {
         self.coords.hash(state)
     }
 }
 
-impl<N: Scalar + Copy, D: DimName> Copy for Point<N, D>
-where
-    DefaultAllocator: Allocator<N, D>,
-    <DefaultAllocator as Allocator<N, D>>::Buffer: Copy,
+impl<N: Scalar + Copy, const D: usize> Copy for Point<N, D>
+// where
+//     DefaultAllocator: Allocator<N, D>,
+//     <DefaultAllocator as Allocator<N, D>>::Buffer: Copy,
 {
 }
 
 #[cfg(feature = "bytemuck")]
-unsafe impl<N: Scalar, D: DimName> bytemuck::Zeroable for Point<N, D>
-where
-    VectorN<N, D>: bytemuck::Zeroable,
-    DefaultAllocator: Allocator<N, D>,
+unsafe impl<N: Scalar, const D: usize> bytemuck::Zeroable for Point<N, D> where
+    VectorN<N, Const<D>>: bytemuck::Zeroable // DefaultAllocator: Allocator<N, D>,
 {
 }
 
 #[cfg(feature = "bytemuck")]
-unsafe impl<N: Scalar, D: DimName> bytemuck::Pod for Point<N, D>
+unsafe impl<N: Scalar, const D: usize> bytemuck::Pod for Point<N, D>
 where
     N: Copy,
-    VectorN<N, D>: bytemuck::Pod,
-    DefaultAllocator: Allocator<N, D>,
-    <DefaultAllocator as Allocator<N, D>>::Buffer: Copy,
+    VectorN<N, Const<D>>: bytemuck::Pod,
+    // DefaultAllocator: Allocator<N, D>,
+    // <DefaultAllocator as Allocator<N, D>>::Buffer: Copy,
 {
 }
 
 #[cfg(feature = "serde-serialize")]
-impl<N: Scalar, D: DimName> Serialize for Point<N, D>
-where
-    DefaultAllocator: Allocator<N, D>,
-    <DefaultAllocator as Allocator<N, D>>::Buffer: Serialize,
+impl<N: Scalar, const D: usize> Serialize for Point<N, D>
+// where
+//     DefaultAllocator: Allocator<N, D>,
+//     <DefaultAllocator as Allocator<N, D>>::Buffer: Serialize,
 {
     fn serialize<S>(&self, serializer: S) -> Result<S::Ok, S::Error>
     where
@@ -98,10 +93,10 @@ where
 }
 
 #[cfg(feature = "serde-serialize")]
-impl<'a, N: Scalar, D: DimName> Deserialize<'a> for Point<N, D>
-where
-    DefaultAllocator: Allocator<N, D>,
-    <DefaultAllocator as Allocator<N, D>>::Buffer: Deserialize<'a>,
+impl<'a, N: Scalar, const D: usize> Deserialize<'a> for Point<N, D>
+// where
+//     DefaultAllocator: Allocator<N, D>,
+//     <DefaultAllocator as Allocator<N, D>>::Buffer: Deserialize<'a>,
 {
     fn deserialize<Des>(deserializer: Des) -> Result<Self, Des::Error>
     where
@@ -114,12 +109,11 @@ where
 }
 
 #[cfg(feature = "abomonation-serialize")]
-impl<N, D> Abomonation for Point<N, D>
+impl<N, const D: usize> Abomonation for Point<N, D>
 where
     N: Scalar,
-    D: DimName,
-    VectorN<N, D>: Abomonation,
-    DefaultAllocator: Allocator<N, D>,
+    VectorN<N, Const<D>>: Abomonation,
+    // DefaultAllocator: Allocator<N, D>,
 {
     unsafe fn entomb<W: Write>(&self, writer: &mut W) -> IOResult<()> {
         self.coords.entomb(writer)
@@ -134,9 +128,9 @@ where
     }
 }
 
-impl<N: Scalar, D: DimName> Point<N, D>
-where
-    DefaultAllocator: Allocator<N, D>,
+impl<N: Scalar, const D: usize> Point<N, D>
+// where
+//     DefaultAllocator: Allocator<N, D>,
 {
     /// Returns a point containing the result of `f` applied to each of its entries.
     ///
@@ -152,8 +146,8 @@ where
     /// ```
     #[inline]
     pub fn map<N2: Scalar, F: FnMut(N) -> N2>(&self, f: F) -> Point<N2, D>
-    where
-        DefaultAllocator: Allocator<N2, D>,
+// where
+    //     DefaultAllocator: Allocator<N2, D>,
     {
         self.coords.map(f).into()
     }
@@ -193,20 +187,21 @@ where
     /// assert_eq!(p.to_homogeneous(), Vector4::new(10.0, 20.0, 30.0, 1.0));
     /// ```
     #[inline]
-    pub fn to_homogeneous(&self) -> VectorN<N, DimNameSum<D, U1>>
+    pub fn to_homogeneous(&self) -> VectorN<N, DimNameSum<Const<D>, U1>>
     where
         N: One,
-        D: DimNameAdd<U1>,
-        DefaultAllocator: Allocator<N, DimNameSum<D, U1>>,
+        Const<D>: DimNameAdd<U1>,
+        DefaultAllocator: Allocator<N, DimNameSum<Const<D>, U1>>,
     {
         let mut res = unsafe {
             crate::unimplemented_or_uninitialized_generic!(
-                <DimNameSum<D, U1> as DimName>::name(),
+                <DimNameSum<Const<D>, U1> as DimName>::name(),
                 Const::<1>
             )
         };
-        res.fixed_slice_mut::<D, U1>(0, 0).copy_from(&self.coords);
-        res[(D::dim(), 0)] = N::one();
+        res.fixed_slice_mut::<Const<D>, U1>(0, 0)
+            .copy_from(&self.coords);
+        res[(D, 0)] = N::one();
 
         res
     }
@@ -214,7 +209,7 @@ where
     /// Creates a new point with the given coordinates.
     #[deprecated(note = "Use Point::from(vector) instead.")]
     #[inline]
-    pub fn from_coordinates(coords: VectorN<N, D>) -> Self {
+    pub fn from_coordinates(coords: VectorN<N, Const<D>>) -> Self {
         Self { coords }
     }
 
@@ -269,7 +264,10 @@ where
     /// assert_eq!(it.next(), Some(3.0));
     /// assert_eq!(it.next(), None);
     #[inline]
-    pub fn iter(&self) -> MatrixIter<N, D, U1, <DefaultAllocator as Allocator<N, D>>::Buffer> {
+    pub fn iter(
+        &self,
+    ) -> MatrixIter<N, Const<D>, Const<1>, <DefaultAllocator as Allocator<N, Const<D>>>::Buffer>
+    {
         self.coords.iter()
     }
 
@@ -294,7 +292,8 @@ where
     #[inline]
     pub fn iter_mut(
         &mut self,
-    ) -> MatrixIterMut<N, D, U1, <DefaultAllocator as Allocator<N, D>>::Buffer> {
+    ) -> MatrixIterMut<N, Const<D>, Const<1>, <DefaultAllocator as Allocator<N, Const<D>>>::Buffer>
+    {
         self.coords.iter_mut()
     }
 
@@ -311,9 +310,9 @@ where
     }
 }
 
-impl<N: Scalar + AbsDiffEq, D: DimName> AbsDiffEq for Point<N, D>
+impl<N: Scalar + AbsDiffEq, const D: usize> AbsDiffEq for Point<N, D>
 where
-    DefaultAllocator: Allocator<N, D>,
+    // DefaultAllocator: Allocator<N, D>,
     N::Epsilon: Copy,
 {
     type Epsilon = N::Epsilon;
@@ -329,9 +328,9 @@ where
     }
 }
 
-impl<N: Scalar + RelativeEq, D: DimName> RelativeEq for Point<N, D>
+impl<N: Scalar + RelativeEq, const D: usize> RelativeEq for Point<N, D>
 where
-    DefaultAllocator: Allocator<N, D>,
+    // DefaultAllocator: Allocator<N, D>,
     N::Epsilon: Copy,
 {
     #[inline]
@@ -351,9 +350,9 @@ where
     }
 }
 
-impl<N: Scalar + UlpsEq, D: DimName> UlpsEq for Point<N, D>
+impl<N: Scalar + UlpsEq, const D: usize> UlpsEq for Point<N, D>
 where
-    DefaultAllocator: Allocator<N, D>,
+    // DefaultAllocator: Allocator<N, D>,
     N::Epsilon: Copy,
 {
     #[inline]
@@ -367,11 +366,14 @@ where
     }
 }
 
-impl<N: Scalar + Eq, D: DimName> Eq for Point<N, D> where DefaultAllocator: Allocator<N, D> {}
+impl<N: Scalar + Eq, const D: usize> Eq for Point<N, D>
+// where DefaultAllocator: Allocator<N, D>
+{
+}
 
-impl<N: Scalar, D: DimName> PartialEq for Point<N, D>
-where
-    DefaultAllocator: Allocator<N, D>,
+impl<N: Scalar, const D: usize> PartialEq for Point<N, D>
+// where
+//     DefaultAllocator: Allocator<N, D>,
 {
     #[inline]
     fn eq(&self, right: &Self) -> bool {
@@ -379,9 +381,9 @@ where
     }
 }
 
-impl<N: Scalar + PartialOrd, D: DimName> PartialOrd for Point<N, D>
-where
-    DefaultAllocator: Allocator<N, D>,
+impl<N: Scalar + PartialOrd, const D: usize> PartialOrd for Point<N, D>
+// where
+//     DefaultAllocator: Allocator<N, D>,
 {
     #[inline]
     fn partial_cmp(&self, other: &Self) -> Option<Ordering> {
@@ -412,9 +414,9 @@ where
 /*
  * inf/sup
  */
-impl<N: Scalar + SimdPartialOrd, D: DimName> Point<N, D>
-where
-    DefaultAllocator: Allocator<N, D>,
+impl<N: Scalar + SimdPartialOrd, const D: usize> Point<N, D>
+// where
+//     DefaultAllocator: Allocator<N, D>,
 {
     /// Computes the infimum (aka. componentwise min) of two points.
     #[inline]
@@ -441,9 +443,9 @@ where
  * Display
  *
  */
-impl<N: Scalar + fmt::Display, D: DimName> fmt::Display for Point<N, D>
-where
-    DefaultAllocator: Allocator<N, D>,
+impl<N: Scalar + fmt::Display, const D: usize> fmt::Display for Point<N, D>
+// where
+//     DefaultAllocator: Allocator<N, D>,
 {
     fn fmt(&self, f: &mut fmt::Formatter) -> fmt::Result {
         write!(f, "{{")?;
diff --git a/src/geometry/point_alias.rs b/src/geometry/point_alias.rs
index 05874ae4..402c1201 100644
--- a/src/geometry/point_alias.rs
+++ b/src/geometry/point_alias.rs
@@ -1,28 +1,26 @@
-use crate::base::dimension::{U1, U2, U3, U4, U5, U6};
-
 use crate::geometry::Point;
 
 /// A statically sized 1-dimensional column point.
 ///
 /// **Because this is an alias, not all its methods are listed here. See the [`Point`](crate::Point) type too.**
-pub type Point1<N> = Point<N, U1>;
+pub type Point1<N> = Point<N, 1>;
 /// A statically sized 2-dimensional column point.
 ///
 /// **Because this is an alias, not all its methods are listed here. See the [`Point`](crate::Point) type too.**
-pub type Point2<N> = Point<N, U2>;
+pub type Point2<N> = Point<N, 2>;
 /// A statically sized 3-dimensional column point.
 ///
 /// **Because this is an alias, not all its methods are listed here. See the [`Point`](crate::Point) type too.**
-pub type Point3<N> = Point<N, U3>;
+pub type Point3<N> = Point<N, 3>;
 /// A statically sized 4-dimensional column point.
 ///
 /// **Because this is an alias, not all its methods are listed here. See the [`Point`](crate::Point) type too.**
-pub type Point4<N> = Point<N, U4>;
+pub type Point4<N> = Point<N, 4>;
 /// A statically sized 5-dimensional column point.
 ///
 /// **Because this is an alias, not all its methods are listed here. See the [`Point`](crate::Point) type too.**
-pub type Point5<N> = Point<N, U5>;
+pub type Point5<N> = Point<N, 5>;
 /// A statically sized 6-dimensional column point.
 ///
 /// **Because this is an alias, not all its methods are listed here. See the [`Point`](crate::Point) type too.**
-pub type Point6<N> = Point<N, U6>;
+pub type Point6<N> = Point<N, 6>;
diff --git a/src/geometry/point_construction.rs b/src/geometry/point_construction.rs
index ad3cb66d..4ddaf1f9 100644
--- a/src/geometry/point_construction.rs
+++ b/src/geometry/point_construction.rs
@@ -9,7 +9,7 @@ use rand::{
 };
 
 use crate::base::allocator::Allocator;
-use crate::base::dimension::{DimName, DimNameAdd, DimNameSum, U1};
+use crate::base::dimension::{DimNameAdd, DimNameSum, U1};
 use crate::base::{DefaultAllocator, Scalar, VectorN};
 use crate::{
     Const, Point1, Point2, Point3, Point4, Point5, Point6, Vector1, Vector2, Vector3, Vector4,
@@ -20,16 +20,15 @@ use simba::scalar::{ClosedDiv, SupersetOf};
 use crate::geometry::Point;
 
 /// # Other construction methods
-impl<N: Scalar, D: DimName> Point<N, D>
-where
-    DefaultAllocator: Allocator<N, D>,
+impl<N: Scalar, const D: usize> Point<N, D>
+// where
+//     DefaultAllocator: Allocator<N, D>,
 {
     /// Creates a new point with uninitialized coordinates.
     #[inline]
     pub unsafe fn new_uninitialized() -> Self {
         Self::from(crate::unimplemented_or_uninitialized_generic!(
-            D::name(),
-            Const::<1>
+            Const::<D>, Const::<1>
         ))
     }
 
@@ -106,14 +105,14 @@ where
     /// assert_eq!(pt, Some(Point2::new(1.0, 2.0)));
     /// ```
     #[inline]
-    pub fn from_homogeneous(v: VectorN<N, DimNameSum<D, U1>>) -> Option<Self>
+    pub fn from_homogeneous(v: VectorN<N, DimNameSum<Const<D>, U1>>) -> Option<Self>
     where
         N: Scalar + Zero + One + ClosedDiv,
-        D: DimNameAdd<U1>,
-        DefaultAllocator: Allocator<N, DimNameSum<D, U1>>,
+        Const<D>: DimNameAdd<U1>,
+        DefaultAllocator: Allocator<N, DimNameSum<Const<D>, U1>>,
     {
-        if !v[D::dim()].is_zero() {
-            let coords = v.fixed_slice::<D, U1>(0, 0) / v[D::dim()].inlined_clone();
+        if !v[D].is_zero() {
+            let coords = v.fixed_slice::<Const<D>, U1>(0, 0) / v[D].inlined_clone();
             Some(Self::from(coords))
         } else {
             None
@@ -132,7 +131,7 @@ where
     pub fn cast<To: Scalar>(self) -> Point<To, D>
     where
         Point<To, D>: SupersetOf<Self>,
-        DefaultAllocator: Allocator<To, D>,
+        // DefaultAllocator: Allocator<To, D>,
     {
         crate::convert(self)
     }
@@ -143,9 +142,9 @@ where
  * Traits that build points.
  *
  */
-impl<N: Scalar + Bounded, D: DimName> Bounded for Point<N, D>
-where
-    DefaultAllocator: Allocator<N, D>,
+impl<N: Scalar + Bounded, const D: usize> Bounded for Point<N, D>
+// where
+//     DefaultAllocator: Allocator<N, D>,
 {
     #[inline]
     fn max_value() -> Self {
@@ -159,9 +158,9 @@ where
 }
 
 #[cfg(feature = "rand-no-std")]
-impl<N: Scalar, D: DimName> Distribution<Point<N, D>> for Standard
+impl<N: Scalar, const D: usize> Distribution<Point<N, D>> for Standard
 where
-    DefaultAllocator: Allocator<N, D>,
+    // DefaultAllocator: Allocator<N, D>,
     Standard: Distribution<N>,
 {
      /// Generate a `Point` where each coordinate is an independent variate from `[0, 1)`.
@@ -172,10 +171,10 @@ where
 }
 
 #[cfg(feature = "arbitrary")]
-impl<N: Scalar + Arbitrary + Send, D: DimName> Arbitrary for Point<N, D>
+impl<N: Scalar + Arbitrary + Send, const D: usize> Arbitrary for Point<N, D>
 where
-    DefaultAllocator: Allocator<N, D>,
-    <DefaultAllocator as Allocator<N, D>>::Buffer: Send,
+    // DefaultAllocator: Allocator<N, D>,
+    <DefaultAllocator as Allocator<N, Const<D>>>::Buffer: Send,
 {
     #[inline]
     fn arbitrary(g: &mut Gen) -> Self {
diff --git a/src/geometry/point_conversion.rs b/src/geometry/point_conversion.rs
index 6f3d865b..e301f948 100644
--- a/src/geometry/point_conversion.rs
+++ b/src/geometry/point_conversion.rs
@@ -3,8 +3,8 @@ use simba::scalar::{ClosedDiv, SubsetOf, SupersetOf};
 use simba::simd::PrimitiveSimdValue;
 
 use crate::base::allocator::Allocator;
-use crate::base::dimension::{DimName, DimNameAdd, DimNameSum, U1};
-use crate::base::{DefaultAllocator, Matrix, Scalar, VectorN};
+use crate::base::dimension::{DimNameAdd, DimNameSum, U1};
+use crate::base::{Const, DefaultAllocator, Matrix, Scalar, VectorN};
 
 use crate::geometry::Point;
 
@@ -16,12 +16,11 @@ use crate::geometry::Point;
  * Point -> Vector (homogeneous)
  */
 
-impl<N1, N2, D> SubsetOf<Point<N2, D>> for Point<N1, D>
+impl<N1, N2, const D: usize> SubsetOf<Point<N2, D>> for Point<N1, D>
 where
-    D: DimName,
     N1: Scalar,
     N2: Scalar + SupersetOf<N1>,
-    DefaultAllocator: Allocator<N2, D> + Allocator<N1, D>,
+    // DefaultAllocator: Allocator<N2, D> + Allocator<N1, D>,
 {
     #[inline]
     fn to_superset(&self) -> Point<N2, D> {
@@ -41,40 +40,41 @@ where
     }
 }
 
-impl<N1, N2, D> SubsetOf<VectorN<N2, DimNameSum<D, U1>>> for Point<N1, D>
+impl<N1, N2, const D: usize> SubsetOf<VectorN<N2, DimNameSum<Const<D>, U1>>> for Point<N1, D>
 where
-    D: DimNameAdd<U1>,
+    Const<D>: DimNameAdd<U1>,
     N1: Scalar,
     N2: Scalar + Zero + One + ClosedDiv + SupersetOf<N1>,
-    DefaultAllocator: Allocator<N1, D>
-        + Allocator<N1, DimNameSum<D, U1>>
-        + Allocator<N2, DimNameSum<D, U1>>
-        + Allocator<N2, D>,
+    DefaultAllocator:
+        Allocator<N1, DimNameSum<Const<D>, U1>> + Allocator<N2, DimNameSum<Const<D>, U1>>,
+    // + Allocator<N1, D>
+    // + Allocator<N2, D>,
 {
     #[inline]
-    fn to_superset(&self) -> VectorN<N2, DimNameSum<D, U1>> {
+    fn to_superset(&self) -> VectorN<N2, DimNameSum<Const<D>, U1>> {
         let p: Point<N2, D> = self.to_superset();
         p.to_homogeneous()
     }
 
     #[inline]
-    fn is_in_subset(v: &VectorN<N2, DimNameSum<D, U1>>) -> bool {
-        crate::is_convertible::<_, VectorN<N1, DimNameSum<D, U1>>>(v) && !v[D::dim()].is_zero()
+    fn is_in_subset(v: &VectorN<N2, DimNameSum<Const<D>, U1>>) -> bool {
+        crate::is_convertible::<_, VectorN<N1, DimNameSum<D, U1>>>(v) && !v[D].is_zero()
     }
 
     #[inline]
-    fn from_superset_unchecked(v: &VectorN<N2, DimNameSum<D, U1>>) -> Self {
-        let coords = v.fixed_slice::<D, U1>(0, 0) / v[D::dim()].inlined_clone();
+    fn from_superset_unchecked(v: &VectorN<N2, DimNameSum<Const<D>, U1>>) -> Self {
+        let coords = v.fixed_slice::<D, U1>(0, 0) / v[D].inlined_clone();
         Self {
             coords: crate::convert_unchecked(coords),
         }
     }
 }
 
-impl<N: Scalar + Zero + One, D: DimName> From<Point<N, D>> for VectorN<N, DimNameSum<D, U1>>
+impl<N: Scalar + Zero + One, const D: usize> From<Point<N, D>>
+    for VectorN<N, DimNameSum<Const<D>, U1>>
 where
-    D: DimNameAdd<U1>,
-    DefaultAllocator: Allocator<N, D> + Allocator<N, DimNameSum<D, U1>>,
+    Const<D>: DimNameAdd<U1>,
+    DefaultAllocator: Allocator<N, DimNameSum<Const<D>, U1>>,
 {
     #[inline]
     fn from(t: Point<N, D>) -> Self {
@@ -82,23 +82,23 @@ where
     }
 }
 
-impl<N: Scalar, D: DimName> From<VectorN<N, D>> for Point<N, D>
-where
-    DefaultAllocator: Allocator<N, D>,
+impl<N: Scalar, const D: usize> From<VectorN<N, Const<D>>> for Point<N, D>
+// where
+//     DefaultAllocator: Allocator<N, D>,
 {
     #[inline]
-    fn from(coords: VectorN<N, D>) -> Self {
+    fn from(coords: VectorN<N, Const<D>>) -> Self {
         Point { coords }
     }
 }
 
-impl<N: Scalar + Copy + PrimitiveSimdValue, D: DimName> From<[Point<N::Element, D>; 2]>
+impl<N: Scalar + Copy + PrimitiveSimdValue, const D: usize> From<[Point<N::Element, D>; 2]>
     for Point<N, D>
 where
     N: From<[<N as simba::simd::SimdValue>::Element; 2]>,
     N::Element: Scalar + Copy,
-    DefaultAllocator: Allocator<N, D> + Allocator<N::Element, D>,
-    <DefaultAllocator as Allocator<N::Element, D>>::Buffer: Copy,
+    // DefaultAllocator: Allocator<N, D> + Allocator<N::Element, D>,
+    <DefaultAllocator as Allocator<N::Element, Const<D>>>::Buffer: Copy,
 {
     #[inline]
     fn from(arr: [Point<N::Element, D>; 2]) -> Self {
@@ -106,13 +106,13 @@ where
     }
 }
 
-impl<N: Scalar + Copy + PrimitiveSimdValue, D: DimName> From<[Point<N::Element, D>; 4]>
+impl<N: Scalar + Copy + PrimitiveSimdValue, const D: usize> From<[Point<N::Element, D>; 4]>
     for Point<N, D>
 where
     N: From<[<N as simba::simd::SimdValue>::Element; 4]>,
     N::Element: Scalar + Copy,
-    DefaultAllocator: Allocator<N, D> + Allocator<N::Element, D>,
-    <DefaultAllocator as Allocator<N::Element, D>>::Buffer: Copy,
+    // DefaultAllocator: Allocator<N, D> + Allocator<N::Element, D>,
+    <DefaultAllocator as Allocator<N::Element, Const<D>>>::Buffer: Copy,
 {
     #[inline]
     fn from(arr: [Point<N::Element, D>; 4]) -> Self {
@@ -125,13 +125,13 @@ where
     }
 }
 
-impl<N: Scalar + Copy + PrimitiveSimdValue, D: DimName> From<[Point<N::Element, D>; 8]>
+impl<N: Scalar + Copy + PrimitiveSimdValue, const D: usize> From<[Point<N::Element, D>; 8]>
     for Point<N, D>
 where
     N: From<[<N as simba::simd::SimdValue>::Element; 8]>,
     N::Element: Scalar + Copy,
-    DefaultAllocator: Allocator<N, D> + Allocator<N::Element, D>,
-    <DefaultAllocator as Allocator<N::Element, D>>::Buffer: Copy,
+    // DefaultAllocator: Allocator<N, D> + Allocator<N::Element, D>,
+    <DefaultAllocator as Allocator<N::Element, Const<D>>>::Buffer: Copy,
 {
     #[inline]
     fn from(arr: [Point<N::Element, D>; 8]) -> Self {
@@ -148,13 +148,13 @@ where
     }
 }
 
-impl<N: Scalar + Copy + PrimitiveSimdValue, D: DimName> From<[Point<N::Element, D>; 16]>
+impl<N: Scalar + Copy + PrimitiveSimdValue, const D: usize> From<[Point<N::Element, D>; 16]>
     for Point<N, D>
 where
     N: From<[<N as simba::simd::SimdValue>::Element; 16]>,
     N::Element: Scalar + Copy,
-    DefaultAllocator: Allocator<N, D> + Allocator<N::Element, D>,
-    <DefaultAllocator as Allocator<N::Element, D>>::Buffer: Copy,
+    // DefaultAllocator: Allocator<N, D> + Allocator<N::Element, D>,
+    <DefaultAllocator as Allocator<N::Element, Const<D>>>::Buffer: Copy,
 {
     #[inline]
     fn from(arr: [Point<N::Element, D>; 16]) -> Self {
diff --git a/src/geometry/point_coordinates.rs b/src/geometry/point_coordinates.rs
index 268c9b0d..3d54d899 100644
--- a/src/geometry/point_coordinates.rs
+++ b/src/geometry/point_coordinates.rs
@@ -1,9 +1,7 @@
 use std::ops::{Deref, DerefMut};
 
-use crate::base::allocator::Allocator;
 use crate::base::coordinates::{X, XY, XYZ, XYZW, XYZWA, XYZWAB};
-use crate::base::dimension::{U1, U2, U3, U4, U5, U6};
-use crate::base::{DefaultAllocator, Scalar};
+use crate::base::Scalar;
 
 use crate::geometry::Point;
 
@@ -14,9 +12,10 @@ use crate::geometry::Point;
  */
 
 macro_rules! deref_impl(
-    ($D: ty, $Target: ident $(, $comps: ident)*) => {
+    ($D: expr, $Target: ident $(, $comps: ident)*) => {
         impl<N: Scalar> Deref for Point<N, $D>
-            where DefaultAllocator: Allocator<N, $D> {
+            // where DefaultAllocator: Allocator<N, $D>
+        {
             type Target = $Target<N>;
 
             #[inline]
@@ -26,7 +25,8 @@ macro_rules! deref_impl(
         }
 
         impl<N: Scalar> DerefMut for Point<N, $D>
-            where DefaultAllocator: Allocator<N, $D> {
+            // where DefaultAllocator: Allocator<N, $D>
+        {
             #[inline]
             fn deref_mut(&mut self) -> &mut Self::Target {
                 &mut *self.coords
@@ -35,9 +35,9 @@ macro_rules! deref_impl(
     }
 );
 
-deref_impl!(U1, X, x);
-deref_impl!(U2, XY, x, y);
-deref_impl!(U3, XYZ, x, y, z);
-deref_impl!(U4, XYZW, x, y, z, w);
-deref_impl!(U5, XYZWA, x, y, z, w, a);
-deref_impl!(U6, XYZWAB, x, y, z, w, a, b);
+deref_impl!(1, X, x);
+deref_impl!(2, XY, x, y);
+deref_impl!(3, XYZ, x, y, z);
+deref_impl!(4, XYZW, x, y, z, w);
+deref_impl!(5, XYZWA, x, y, z, w, a);
+deref_impl!(6, XYZWAB, x, y, z, w, a, b);
diff --git a/src/geometry/point_ops.rs b/src/geometry/point_ops.rs
index 029286ff..48af3a8d 100644
--- a/src/geometry/point_ops.rs
+++ b/src/geometry/point_ops.rs
@@ -11,7 +11,7 @@ use crate::base::constraint::{
 };
 use crate::base::dimension::{Dim, DimName, U1};
 use crate::base::storage::Storage;
-use crate::base::{DefaultAllocator, Matrix, Scalar, Vector, VectorSum};
+use crate::base::{Const, DefaultAllocator, Matrix, Scalar, Vector, VectorSum};
 
 use crate::geometry::Point;
 
@@ -20,9 +20,9 @@ use crate::geometry::Point;
  * Indexing.
  *
  */
-impl<N: Scalar, D: DimName> Index<usize> for Point<N, D>
-where
-    DefaultAllocator: Allocator<N, D>,
+impl<N: Scalar, const D: usize> Index<usize> for Point<N, D>
+// where
+//     DefaultAllocator: Allocator<N, D>,
 {
     type Output = N;
 
@@ -32,9 +32,9 @@ where
     }
 }
 
-impl<N: Scalar, D: DimName> IndexMut<usize> for Point<N, D>
-where
-    DefaultAllocator: Allocator<N, D>,
+impl<N: Scalar, const D: usize> IndexMut<usize> for Point<N, D>
+// where
+//     DefaultAllocator: Allocator<N, D>,
 {
     #[inline]
     fn index_mut(&mut self, i: usize) -> &mut Self::Output {
@@ -47,9 +47,9 @@ where
  * Neg.
  *
  */
-impl<N: Scalar + ClosedNeg, D: DimName> Neg for Point<N, D>
-where
-    DefaultAllocator: Allocator<N, D>,
+impl<N: Scalar + ClosedNeg, const D: usize> Neg for Point<N, D>
+// where
+//     DefaultAllocator: Allocator<N, D>,
 {
     type Output = Self;
 
@@ -59,9 +59,9 @@ where
     }
 }
 
-impl<'a, N: Scalar + ClosedNeg, D: DimName> Neg for &'a Point<N, D>
-where
-    DefaultAllocator: Allocator<N, D>,
+impl<'a, N: Scalar + ClosedNeg, const D: usize> Neg for &'a Point<N, D>
+// where
+//     DefaultAllocator: Allocator<N, D>,
 {
     type Output = Point<N, D>;
 
@@ -79,22 +79,22 @@ where
 
 // Point - Point
 add_sub_impl!(Sub, sub, ClosedSub;
-    (D, U1), (D, U1) for D: DimName;
+    (D, U1), (D, U1);
     self: &'a Point<N, D>, right: &'b Point<N, D>, Output = VectorSum<N, D, D>;
     &self.coords - &right.coords; 'a, 'b);
 
 add_sub_impl!(Sub, sub, ClosedSub;
-    (D, U1), (D, U1) for D: DimName;
+    (D, U1), (D, U1);
     self: &'a Point<N, D>, right: Point<N, D>, Output = VectorSum<N, D, D>;
     &self.coords - right.coords; 'a);
 
 add_sub_impl!(Sub, sub, ClosedSub;
-    (D, U1), (D, U1) for D: DimName;
+    (D, U1), (D, U1);
     self: Point<N, D>, right: &'b Point<N, D>, Output = VectorSum<N, D, D>;
     self.coords - &right.coords; 'b);
 
 add_sub_impl!(Sub, sub, ClosedSub;
-    (D, U1), (D, U1) for D: DimName;
+    (D, U1), (D, U1);
     self: Point<N, D>, right: Point<N, D>, Output = VectorSum<N, D, D>;
     self.coords - right.coords; );
 
@@ -143,11 +143,11 @@ add_sub_impl!(Add, add, ClosedAdd;
 // XXX: replace by the shared macro: add_sub_assign_impl
 macro_rules! op_assign_impl(
     ($($TraitAssign: ident, $method_assign: ident, $bound: ident);* $(;)*) => {$(
-        impl<'b, N, D1: DimName, D2: Dim, SB> $TraitAssign<&'b Vector<N, D2, SB>> for Point<N, D1>
+        impl<'b, N, D2: Dim, SB, const D1: usize> $TraitAssign<&'b Vector<N, D2, SB>> for Point<N, D1>
             where N: Scalar + $bound,
                   SB: Storage<N, D2>,
-                  DefaultAllocator: Allocator<N, D1>,
-                  ShapeConstraint: SameNumberOfRows<D1, D2> {
+                  // DefaultAllocator: Allocator<N, D1>,
+                  ShapeConstraint: SameNumberOfRows<Const<D1>, D2> {
 
             #[inline]
             fn $method_assign(&mut self, right: &'b Vector<N, D2, SB>) {
@@ -155,10 +155,10 @@ macro_rules! op_assign_impl(
             }
         }
 
-        impl<N, D1: DimName, D2: Dim, SB> $TraitAssign<Vector<N, D2, SB>> for Point<N, D1>
+        impl<N, D2: Dim, SB, const D1: usize> $TraitAssign<Vector<N, D2, SB>> for Point<N, D1>
             where N: Scalar + $bound,
                   SB: Storage<N, D2>,
-                  DefaultAllocator: Allocator<N, D1>,
+                  // DefaultAllocator: Allocator<N, D1>,
                   ShapeConstraint: SameNumberOfRows<D1, D2> {
 
             #[inline]
@@ -198,8 +198,9 @@ md_impl_all!(
 macro_rules! componentwise_scalarop_impl(
     ($Trait: ident, $method: ident, $bound: ident;
      $TraitAssign: ident, $method_assign: ident) => {
-        impl<N: Scalar + $bound, D: DimName> $Trait<N> for Point<N, D>
-            where DefaultAllocator: Allocator<N, D> {
+        impl<N: Scalar + $bound, const D: usize> $Trait<N> for Point<N, D>
+            // where DefaultAllocator: Allocator<N, D>
+        {
             type Output = Point<N, D>;
 
             #[inline]
@@ -208,8 +209,9 @@ macro_rules! componentwise_scalarop_impl(
             }
         }
 
-        impl<'a, N: Scalar + $bound, D: DimName> $Trait<N> for &'a Point<N, D>
-            where DefaultAllocator: Allocator<N, D> {
+        impl<'a, N: Scalar + $bound, const D: usize> $Trait<N> for &'a Point<N, D>
+            // where DefaultAllocator: Allocator<N, D>
+        {
             type Output = Point<N, D>;
 
             #[inline]
@@ -218,8 +220,9 @@ macro_rules! componentwise_scalarop_impl(
             }
         }
 
-        impl<N: Scalar + $bound, D: DimName> $TraitAssign<N> for Point<N, D>
-            where DefaultAllocator: Allocator<N, D> {
+        impl<N: Scalar + $bound, const D: usize> $TraitAssign<N> for Point<N, D>
+            /* where DefaultAllocator: Allocator<N, D> */
+        {
             #[inline]
             fn $method_assign(&mut self, right: N) {
                 self.coords.$method_assign(right)
@@ -233,8 +236,9 @@ componentwise_scalarop_impl!(Div, div, ClosedDiv; DivAssign, div_assign);
 
 macro_rules! left_scalar_mul_impl(
     ($($T: ty),* $(,)*) => {$(
-        impl<D: DimName> Mul<Point<$T, D>> for $T
-            where DefaultAllocator: Allocator<$T, D> {
+        impl<const D: usize> Mul<Point<$T, D>> for $T
+           // where DefaultAllocator: Allocator<$T, D>
+        {
             type Output = Point<$T, D>;
 
             #[inline]
@@ -243,8 +247,9 @@ macro_rules! left_scalar_mul_impl(
             }
         }
 
-        impl<'b, D: DimName> Mul<&'b Point<$T, D>> for $T
-            where DefaultAllocator: Allocator<$T, D> {
+        impl<'b, const D: usize> Mul<&'b Point<$T, D>> for $T
+            // where DefaultAllocator: Allocator<$T, D>
+        {
             type Output = Point<$T, D>;
 
             #[inline]
diff --git a/src/geometry/point_simba.rs b/src/geometry/point_simba.rs
index a6c8465e..c597d142 100644
--- a/src/geometry/point_simba.rs
+++ b/src/geometry/point_simba.rs
@@ -1,15 +1,13 @@
 use simba::simd::SimdValue;
 
-use crate::base::allocator::Allocator;
-use crate::base::dimension::DimName;
-use crate::base::{DefaultAllocator, Scalar, VectorN};
+use crate::base::{Scalar, VectorN};
 
 use crate::geometry::Point;
 
-impl<N: Scalar + SimdValue, D: DimName> SimdValue for Point<N, D>
+impl<N: Scalar + SimdValue, const D: usize> SimdValue for Point<N, D>
 where
     N::Element: Scalar,
-    DefaultAllocator: Allocator<N, D> + Allocator<N::Element, D>,
+    // DefaultAllocator: Allocator<N, D> + Allocator<N::Element, D>,
 {
     type Element = Point<N::Element, D>;
     type SimdBool = N::SimdBool;
diff --git a/src/geometry/quaternion.rs b/src/geometry/quaternion.rs
index 172f2e66..48a2d2ca 100755
--- a/src/geometry/quaternion.rs
+++ b/src/geometry/quaternion.rs
@@ -1367,7 +1367,7 @@ where
     /// assert_relative_eq!(*rot.matrix(), expected, epsilon = 1.0e-6);
     /// ```
     #[inline]
-    pub fn to_rotation_matrix(&self) -> Rotation<N, U3> {
+    pub fn to_rotation_matrix(&self) -> Rotation<N, 3> {
         let i = self.as_ref()[0];
         let j = self.as_ref()[1];
         let k = self.as_ref()[2];
diff --git a/src/geometry/quaternion_conversion.rs b/src/geometry/quaternion_conversion.rs
index c8b5c6ed..c1b18221 100644
--- a/src/geometry/quaternion_conversion.rs
+++ b/src/geometry/quaternion_conversion.rs
@@ -3,7 +3,6 @@ use num::Zero;
 use simba::scalar::{RealField, SubsetOf, SupersetOf};
 use simba::simd::{PrimitiveSimdValue, SimdRealField, SimdValue};
 
-use crate::base::dimension::U3;
 use crate::base::{Matrix3, Matrix4, Scalar, Vector4};
 use crate::geometry::{
     AbstractRotation, Isometry, Quaternion, Rotation, Rotation3, Similarity, SuperTCategoryOf,
@@ -16,11 +15,11 @@ use crate::geometry::{
  *
  * Quaternion     -> Quaternion
  * UnitQuaternion -> UnitQuaternion
- * UnitQuaternion -> Rotation<U3>
- * UnitQuaternion -> Isometry<U3>
+ * UnitQuaternion -> Rotation<3>
+ * UnitQuaternion -> Isometry<3>
  * UnitQuaternion -> UnitDualQuaternion
- * UnitQuaternion -> Similarity<U3>
- * UnitQuaternion -> Transform<U3>
+ * UnitQuaternion -> Similarity<3>
+ * UnitQuaternion -> Transform<3>
  * UnitQuaternion -> Matrix<U4> (homogeneous)
  *
  * NOTE:
@@ -71,7 +70,7 @@ where
     }
 }
 
-impl<N1, N2> SubsetOf<Rotation<N2, U3>> for UnitQuaternion<N1>
+impl<N1, N2> SubsetOf<Rotation<N2, 3>> for UnitQuaternion<N1>
 where
     N1: RealField,
     N2: RealField + SupersetOf<N1>,
@@ -94,24 +93,24 @@ where
     }
 }
 
-impl<N1, N2, R> SubsetOf<Isometry<N2, U3, R>> for UnitQuaternion<N1>
+impl<N1, N2, R> SubsetOf<Isometry<N2, R, 3>> for UnitQuaternion<N1>
 where
     N1: RealField,
     N2: RealField + SupersetOf<N1>,
-    R: AbstractRotation<N2, U3> + SupersetOf<Self>,
+    R: AbstractRotation<N2, 3> + SupersetOf<Self>,
 {
     #[inline]
-    fn to_superset(&self) -> Isometry<N2, U3, R> {
+    fn to_superset(&self) -> Isometry<N2, R, 3> {
         Isometry::from_parts(Translation::identity(), crate::convert_ref(self))
     }
 
     #[inline]
-    fn is_in_subset(iso: &Isometry<N2, U3, R>) -> bool {
+    fn is_in_subset(iso: &Isometry<N2, R, 3>) -> bool {
         iso.translation.vector.is_zero()
     }
 
     #[inline]
-    fn from_superset_unchecked(iso: &Isometry<N2, U3, R>) -> Self {
+    fn from_superset_unchecked(iso: &Isometry<N2, R, 3>) -> Self {
         crate::convert_ref_unchecked(&iso.rotation)
     }
 }
@@ -138,46 +137,46 @@ where
     }
 }
 
-impl<N1, N2, R> SubsetOf<Similarity<N2, U3, R>> for UnitQuaternion<N1>
+impl<N1, N2, R> SubsetOf<Similarity<N2, R, 3>> for UnitQuaternion<N1>
 where
     N1: RealField,
     N2: RealField + SupersetOf<N1>,
-    R: AbstractRotation<N2, U3> + SupersetOf<Self>,
+    R: AbstractRotation<N2, 3> + SupersetOf<Self>,
 {
     #[inline]
-    fn to_superset(&self) -> Similarity<N2, U3, R> {
+    fn to_superset(&self) -> Similarity<N2, R, 3> {
         Similarity::from_isometry(crate::convert_ref(self), N2::one())
     }
 
     #[inline]
-    fn is_in_subset(sim: &Similarity<N2, U3, R>) -> bool {
+    fn is_in_subset(sim: &Similarity<N2, R, 3>) -> bool {
         sim.isometry.translation.vector.is_zero() && sim.scaling() == N2::one()
     }
 
     #[inline]
-    fn from_superset_unchecked(sim: &Similarity<N2, U3, R>) -> Self {
+    fn from_superset_unchecked(sim: &Similarity<N2, R, 3>) -> Self {
         crate::convert_ref_unchecked(&sim.isometry)
     }
 }
 
-impl<N1, N2, C> SubsetOf<Transform<N2, U3, C>> for UnitQuaternion<N1>
+impl<N1, N2, C> SubsetOf<Transform<N2, C, 3>> for UnitQuaternion<N1>
 where
     N1: RealField,
     N2: RealField + SupersetOf<N1>,
     C: SuperTCategoryOf<TAffine>,
 {
     #[inline]
-    fn to_superset(&self) -> Transform<N2, U3, C> {
+    fn to_superset(&self) -> Transform<N2, C, 3> {
         Transform::from_matrix_unchecked(self.to_homogeneous().to_superset())
     }
 
     #[inline]
-    fn is_in_subset(t: &Transform<N2, U3, C>) -> bool {
+    fn is_in_subset(t: &Transform<N2, C, 3>) -> bool {
         <Self as SubsetOf<_>>::is_in_subset(t.matrix())
     }
 
     #[inline]
-    fn from_superset_unchecked(t: &Transform<N2, U3, C>) -> Self {
+    fn from_superset_unchecked(t: &Transform<N2, C, 3>) -> Self {
         Self::from_superset_unchecked(t.matrix())
     }
 }
diff --git a/src/geometry/reflection.rs b/src/geometry/reflection.rs
index d5e950ec..7ed220ca 100644
--- a/src/geometry/reflection.rs
+++ b/src/geometry/reflection.rs
@@ -1,7 +1,6 @@
-use crate::base::allocator::Allocator;
 use crate::base::constraint::{AreMultipliable, DimEq, SameNumberOfRows, ShapeConstraint};
-use crate::base::{DefaultAllocator, Matrix, Scalar, Unit, Vector};
-use crate::dimension::{Dim, DimName, U1};
+use crate::base::{Const, Matrix, Scalar, Unit, Vector};
+use crate::dimension::{Dim, U1};
 use crate::storage::{Storage, StorageMut};
 use simba::scalar::ComplexField;
 
@@ -13,6 +12,15 @@ pub struct Reflection<N: Scalar, D: Dim, S: Storage<N, D>> {
     bias: N,
 }
 
+impl<N: ComplexField, S: Storage<N, Const<D>>, const D: usize> Reflection<N, Const<D>, S> {
+    /// Creates a new reflection wrt. the plane orthogonal to the given axis and that contains the
+    /// point `pt`.
+    pub fn new_containing_point(axis: Unit<Vector<N, Const<D>, S>>, pt: &Point<N, D>) -> Self {
+        let bias = axis.dotc(&pt.coords);
+        Self::new(axis, bias)
+    }
+}
+
 impl<N: ComplexField, D: Dim, S: Storage<N, D>> Reflection<N, D, S> {
     /// Creates a new reflection wrt the plane orthogonal to the given axis and bias.
     ///
@@ -25,17 +33,6 @@ impl<N: ComplexField, D: Dim, S: Storage<N, D>> Reflection<N, D, S> {
         }
     }
 
-    /// Creates a new reflection wrt. the plane orthogonal to the given axis and that contains the
-    /// point `pt`.
-    pub fn new_containing_point(axis: Unit<Vector<N, D, S>>, pt: &Point<N, D>) -> Self
-    where
-        D: DimName,
-        DefaultAllocator: Allocator<N, D>,
-    {
-        let bias = axis.dotc(&pt.coords);
-        Self::new(axis, bias)
-    }
-
     /// The reflexion axis.
     pub fn axis(&self) -> &Vector<N, D, S> {
         &self.axis
diff --git a/src/geometry/rotation.rs b/src/geometry/rotation.rs
index e4f69fe6..498886d3 100755
--- a/src/geometry/rotation.rs
+++ b/src/geometry/rotation.rs
@@ -18,8 +18,8 @@ use simba::scalar::RealField;
 use simba::simd::SimdRealField;
 
 use crate::base::allocator::Allocator;
-use crate::base::dimension::{DimName, DimNameAdd, DimNameSum, U1};
-use crate::base::{DefaultAllocator, MatrixN, Scalar, Unit, VectorN};
+use crate::base::dimension::{DimNameAdd, DimNameSum, U1};
+use crate::base::{CMatrixN, CVectorN, Const, DefaultAllocator, MatrixN, Scalar, Unit};
 use crate::geometry::Point;
 
 /// A rotation matrix.
@@ -55,34 +55,33 @@ use crate::geometry::Point;
 ///
 #[repr(C)]
 #[derive(Debug)]
-pub struct Rotation<N: Scalar, D: DimName>
-where
-    DefaultAllocator: Allocator<N, D, D>,
+pub struct Rotation<N: Scalar, const D: usize>
+// where
+//     DefaultAllocator: Allocator<N, D, D>,
 {
-    matrix: MatrixN<N, D>,
+    matrix: CMatrixN<N, D>,
 }
 
-impl<N: Scalar + hash::Hash, D: DimName + hash::Hash> hash::Hash for Rotation<N, D>
+impl<N: Scalar + hash::Hash, const D: usize> hash::Hash for Rotation<N, D>
 where
-    DefaultAllocator: Allocator<N, D, D>,
-    <DefaultAllocator as Allocator<N, D, D>>::Buffer: hash::Hash,
+    // DefaultAllocator: Allocator<N, D, D>,
+    <DefaultAllocator as Allocator<N, Const<D>, Const<D>>>::Buffer: hash::Hash,
 {
     fn hash<H: hash::Hasher>(&self, state: &mut H) {
         self.matrix.hash(state)
     }
 }
 
-impl<N: Scalar + Copy, D: DimName> Copy for Rotation<N, D>
-where
-    DefaultAllocator: Allocator<N, D, D>,
-    <DefaultAllocator as Allocator<N, D, D>>::Buffer: Copy,
+impl<N: Scalar + Copy, const D: usize> Copy for Rotation<N, D> where
+    // DefaultAllocator: Allocator<N, D, D>,
+    <DefaultAllocator as Allocator<N, Const<D>, Const<D>>>::Buffer: Copy
 {
 }
 
-impl<N: Scalar, D: DimName> Clone for Rotation<N, D>
+impl<N: Scalar, const D: usize> Clone for Rotation<N, D>
 where
-    DefaultAllocator: Allocator<N, D, D>,
-    <DefaultAllocator as Allocator<N, D, D>>::Buffer: Clone,
+    // DefaultAllocator: Allocator<N, D, D>,
+    <DefaultAllocator as Allocator<N, Const<D>, Const<D>>>::Buffer: Clone,
 {
     #[inline]
     fn clone(&self) -> Self {
@@ -91,12 +90,11 @@ where
 }
 
 #[cfg(feature = "abomonation-serialize")]
-impl<N, D> Abomonation for Rotation<N, D>
+impl<N, const D: usize> Abomonation for Rotation<N, D>
 where
     N: Scalar,
-    D: DimName,
-    MatrixN<N, D>: Abomonation,
-    DefaultAllocator: Allocator<N, D, D>,
+    CMatrixN<N, Const<D>>: Abomonation,
+    // DefaultAllocator: Allocator<N, D, D>,
 {
     unsafe fn entomb<W: Write>(&self, writer: &mut W) -> IOResult<()> {
         self.matrix.entomb(writer)
@@ -112,9 +110,9 @@ where
 }
 
 #[cfg(feature = "serde-serialize")]
-impl<N: Scalar, D: DimName> Serialize for Rotation<N, D>
+impl<N: Scalar, const D: usize> Serialize for Rotation<N, D>
 where
-    DefaultAllocator: Allocator<N, D, D>,
+    // DefaultAllocator: Allocator<N, D, D>,
     Owned<N, D, D>: Serialize,
 {
     fn serialize<S>(&self, serializer: S) -> Result<S::Ok, S::Error>
@@ -126,24 +124,24 @@ where
 }
 
 #[cfg(feature = "serde-serialize")]
-impl<'a, N: Scalar, D: DimName> Deserialize<'a> for Rotation<N, D>
+impl<'a, N: Scalar, const D: usize> Deserialize<'a> for Rotation<N, D>
 where
-    DefaultAllocator: Allocator<N, D, D>,
+    // DefaultAllocator: Allocator<N, D, D>,
     Owned<N, D, D>: Deserialize<'a>,
 {
     fn deserialize<Des>(deserializer: Des) -> Result<Self, Des::Error>
     where
         Des: Deserializer<'a>,
     {
-        let matrix = MatrixN::<N, D>::deserialize(deserializer)?;
+        let matrix = CMatrixN::<N, D>::deserialize(deserializer)?;
 
         Ok(Self::from_matrix_unchecked(matrix))
     }
 }
 
-impl<N: Scalar, D: DimName> Rotation<N, D>
-where
-    DefaultAllocator: Allocator<N, D, D>,
+impl<N: Scalar, const D: usize> Rotation<N, D>
+// where
+//     DefaultAllocator: Allocator<N, D, D>,
 {
     /// Creates a new rotation from the given square matrix.
     ///
@@ -168,7 +166,7 @@ where
     /// assert_eq!(*rot.matrix(), mat);
     /// ```
     #[inline]
-    pub fn from_matrix_unchecked(matrix: MatrixN<N, D>) -> Self {
+    pub fn from_matrix_unchecked(matrix: CMatrixN<N, D>) -> Self {
         assert!(
             matrix.is_square(),
             "Unable to create a rotation from a non-square matrix."
@@ -179,9 +177,9 @@ where
 }
 
 /// # Conversion to a matrix
-impl<N: Scalar, D: DimName> Rotation<N, D>
-where
-    DefaultAllocator: Allocator<N, D, D>,
+impl<N: Scalar, const D: usize> Rotation<N, D>
+// where
+//     DefaultAllocator: Allocator<N, D, D>,
 {
     /// A reference to the underlying matrix representation of this rotation.
     ///
@@ -202,14 +200,14 @@ where
     /// assert_eq!(*rot.matrix(), expected);
     /// ```
     #[inline]
-    pub fn matrix(&self) -> &MatrixN<N, D> {
+    pub fn matrix(&self) -> &CMatrixN<N, D> {
         &self.matrix
     }
 
     /// A mutable reference to the underlying matrix representation of this rotation.
     #[inline]
     #[deprecated(note = "Use `.matrix_mut_unchecked()` instead.")]
-    pub unsafe fn matrix_mut(&mut self) -> &mut MatrixN<N, D> {
+    pub unsafe fn matrix_mut(&mut self) -> &mut CMatrixN<N, D> {
         &mut self.matrix
     }
 
@@ -219,7 +217,7 @@ where
     /// non-square, non-inversible, or non-orthonormal. If one of those properties is broken,
     /// subsequent method calls may be UB.
     #[inline]
-    pub fn matrix_mut_unchecked(&mut self) -> &mut MatrixN<N, D> {
+    pub fn matrix_mut_unchecked(&mut self) -> &mut CMatrixN<N, D> {
         &mut self.matrix
     }
 
@@ -244,7 +242,7 @@ where
     /// assert_eq!(mat, expected);
     /// ```
     #[inline]
-    pub fn into_inner(self) -> MatrixN<N, D> {
+    pub fn into_inner(self) -> CMatrixN<N, D> {
         self.matrix
     }
 
@@ -252,7 +250,7 @@ where
     /// Deprecated: Use [Rotation::into_inner] instead.
     #[deprecated(note = "use `.into_inner()` instead")]
     #[inline]
-    pub fn unwrap(self) -> MatrixN<N, D> {
+    pub fn unwrap(self) -> CMatrixN<N, D> {
         self.matrix
     }
 
@@ -279,13 +277,13 @@ where
     /// assert_eq!(rot.to_homogeneous(), expected);
     /// ```
     #[inline]
-    pub fn to_homogeneous(&self) -> MatrixN<N, DimNameSum<D, U1>>
+    pub fn to_homogeneous(&self) -> MatrixN<N, DimNameSum<Const<D>, U1>>
     where
         N: Zero + One,
-        D: DimNameAdd<U1>,
-        DefaultAllocator: Allocator<N, DimNameSum<D, U1>, DimNameSum<D, U1>>,
+        Const<D>: DimNameAdd<U1>,
+        DefaultAllocator: Allocator<N, DimNameSum<Const<D>, U1>, DimNameSum<Const<D>, U1>>,
     {
-        // We could use `MatrixN::to_homogeneous()` here, but that would imply
+        // We could use `CMatrixN::to_homogeneous()` here, but that would imply
         // adding the additional traits `DimAdd` and `IsNotStaticOne`. Maybe
         // these things will get nicer once specialization lands in Rust.
         let mut res = MatrixN::<N, DimNameSum<D, U1>>::identity();
@@ -296,9 +294,9 @@ where
 }
 
 /// # Transposition and inversion
-impl<N: Scalar, D: DimName> Rotation<N, D>
-where
-    DefaultAllocator: Allocator<N, D, D>,
+impl<N: Scalar, const D: usize> Rotation<N, D>
+// where
+//     DefaultAllocator: Allocator<N, D, D>,
 {
     /// Transposes `self`.
     ///
@@ -404,10 +402,10 @@ where
 }
 
 /// # Transformation of a vector or a point
-impl<N: SimdRealField, D: DimName> Rotation<N, D>
+impl<N: SimdRealField, const D: usize> Rotation<N, D>
 where
     N::Element: SimdRealField,
-    DefaultAllocator: Allocator<N, D, D> + Allocator<N, D>,
+    // DefaultAllocator: Allocator<N, D, D> + Allocator<N, D>,
 {
     /// Rotate the given point.
     ///
@@ -443,7 +441,7 @@ where
     /// assert_relative_eq!(transformed_vector, Vector3::new(3.0, 2.0, -1.0), epsilon = 1.0e-6);
     /// ```
     #[inline]
-    pub fn transform_vector(&self, v: &VectorN<N, D>) -> VectorN<N, D> {
+    pub fn transform_vector(&self, v: &CVectorN<N, D>) -> CVectorN<N, D> {
         self * v
     }
 
@@ -481,7 +479,7 @@ where
     /// assert_relative_eq!(transformed_vector, Vector3::new(-3.0, 2.0, 1.0), epsilon = 1.0e-6);
     /// ```
     #[inline]
-    pub fn inverse_transform_vector(&self, v: &VectorN<N, D>) -> VectorN<N, D> {
+    pub fn inverse_transform_vector(&self, v: &CVectorN<N, D>) -> CVectorN<N, D> {
         self.matrix().tr_mul(v)
     }
 
@@ -500,16 +498,19 @@ where
     /// assert_relative_eq!(transformed_vector, -Vector3::y_axis(), epsilon = 1.0e-6);
     /// ```
     #[inline]
-    pub fn inverse_transform_unit_vector(&self, v: &Unit<VectorN<N, D>>) -> Unit<VectorN<N, D>> {
+    pub fn inverse_transform_unit_vector(&self, v: &Unit<CVectorN<N, D>>) -> Unit<CVectorN<N, D>> {
         Unit::new_unchecked(self.inverse_transform_vector(&**v))
     }
 }
 
-impl<N: Scalar + Eq, D: DimName> Eq for Rotation<N, D> where DefaultAllocator: Allocator<N, D, D> {}
+impl<N: Scalar + Eq, const D: usize> Eq for Rotation<N, D>
+// where DefaultAllocator: Allocator<N, D, D>
+{
+}
 
-impl<N: Scalar + PartialEq, D: DimName> PartialEq for Rotation<N, D>
-where
-    DefaultAllocator: Allocator<N, D, D>,
+impl<N: Scalar + PartialEq, const D: usize> PartialEq for Rotation<N, D>
+// where
+//     DefaultAllocator: Allocator<N, D, D>,
 {
     #[inline]
     fn eq(&self, right: &Self) -> bool {
@@ -517,10 +518,10 @@ where
     }
 }
 
-impl<N, D: DimName> AbsDiffEq for Rotation<N, D>
+impl<N, const D: usize> AbsDiffEq for Rotation<N, D>
 where
     N: Scalar + AbsDiffEq,
-    DefaultAllocator: Allocator<N, D, D>,
+    // DefaultAllocator: Allocator<N, D, D>,
     N::Epsilon: Copy,
 {
     type Epsilon = N::Epsilon;
@@ -536,10 +537,10 @@ where
     }
 }
 
-impl<N, D: DimName> RelativeEq for Rotation<N, D>
+impl<N, const D: usize> RelativeEq for Rotation<N, D>
 where
     N: Scalar + RelativeEq,
-    DefaultAllocator: Allocator<N, D, D>,
+    // DefaultAllocator: Allocator<N, D, D>,
     N::Epsilon: Copy,
 {
     #[inline]
@@ -559,10 +560,10 @@ where
     }
 }
 
-impl<N, D: DimName> UlpsEq for Rotation<N, D>
+impl<N, const D: usize> UlpsEq for Rotation<N, D>
 where
     N: Scalar + UlpsEq,
-    DefaultAllocator: Allocator<N, D, D>,
+    // DefaultAllocator: Allocator<N, D, D>,
     N::Epsilon: Copy,
 {
     #[inline]
@@ -581,10 +582,10 @@ where
  * Display
  *
  */
-impl<N, D: DimName> fmt::Display for Rotation<N, D>
+impl<N, const D: usize> fmt::Display for Rotation<N, D>
 where
     N: RealField + fmt::Display,
-    DefaultAllocator: Allocator<N, D, D> + Allocator<usize, D, D>,
+    // DefaultAllocator: Allocator<N, D, D> + Allocator<usize, D, D>,
 {
     fn fmt(&self, f: &mut fmt::Formatter) -> fmt::Result {
         let precision = f.precision().unwrap_or(3);
diff --git a/src/geometry/rotation_alias.rs b/src/geometry/rotation_alias.rs
index f9e0230b..09d86152 100644
--- a/src/geometry/rotation_alias.rs
+++ b/src/geometry/rotation_alias.rs
@@ -1,13 +1,11 @@
-use crate::base::dimension::{U2, U3};
-
 use crate::geometry::Rotation;
 
 /// A 2-dimensional rotation matrix.
 ///
 /// **Because this is an alias, not all its methods are listed here. See the [`Rotation`](crate::Rotation) type too.**
-pub type Rotation2<N> = Rotation<N, U2>;
+pub type Rotation2<N> = Rotation<N, 2>;
 
 /// A 3-dimensional rotation matrix.
 ///
 /// **Because this is an alias, not all its methods are listed here. See the [`Rotation`](crate::Rotation) type too.**
-pub type Rotation3<N> = Rotation<N, U3>;
+pub type Rotation3<N> = Rotation<N, 3>;
diff --git a/src/geometry/rotation_construction.rs b/src/geometry/rotation_construction.rs
index f198fc92..a144a537 100644
--- a/src/geometry/rotation_construction.rs
+++ b/src/geometry/rotation_construction.rs
@@ -2,17 +2,15 @@ use num::{One, Zero};
 
 use simba::scalar::{ClosedAdd, ClosedMul, SupersetOf};
 
-use crate::base::allocator::Allocator;
-use crate::base::dimension::DimName;
-use crate::base::{DefaultAllocator, MatrixN, Scalar};
+use crate::base::{MatrixN, Scalar};
 
 use crate::geometry::Rotation;
 
 /// # Identity
-impl<N, D: DimName> Rotation<N, D>
+impl<N, const D: usize> Rotation<N, D>
 where
     N: Scalar + Zero + One,
-    DefaultAllocator: Allocator<N, D, D>,
+    // DefaultAllocator: Allocator<N, D, D>,
 {
     /// Creates a new square identity rotation of the given `dimension`.
     ///
@@ -31,9 +29,9 @@ where
     }
 }
 
-impl<N: Scalar, D: DimName> Rotation<N, D>
-where
-    DefaultAllocator: Allocator<N, D, D>,
+impl<N: Scalar, const D: usize> Rotation<N, D>
+// where
+//     DefaultAllocator: Allocator<N, D, D>,
 {
     /// Cast the components of `self` to another type.
     ///
@@ -47,16 +45,16 @@ where
     pub fn cast<To: Scalar>(self) -> Rotation<To, D>
     where
         Rotation<To, D>: SupersetOf<Self>,
-        DefaultAllocator: Allocator<To, D, D>,
+        // DefaultAllocator: Allocator<To, D, D>,
     {
         crate::convert(self)
     }
 }
 
-impl<N, D: DimName> One for Rotation<N, D>
+impl<N, const D: usize> One for Rotation<N, D>
 where
     N: Scalar + Zero + One + ClosedAdd + ClosedMul,
-    DefaultAllocator: Allocator<N, D, D>,
+    // DefaultAllocator: Allocator<N, D, D>,
 {
     #[inline]
     fn one() -> Self {
diff --git a/src/geometry/rotation_conversion.rs b/src/geometry/rotation_conversion.rs
index 21f5a936..14cb296b 100644
--- a/src/geometry/rotation_conversion.rs
+++ b/src/geometry/rotation_conversion.rs
@@ -4,8 +4,8 @@ use simba::scalar::{RealField, SubsetOf, SupersetOf};
 use simba::simd::{PrimitiveSimdValue, SimdValue};
 
 use crate::base::allocator::Allocator;
-use crate::base::dimension::{DimMin, DimName, DimNameAdd, DimNameSum, U1};
-use crate::base::{DefaultAllocator, Matrix2, Matrix3, Matrix4, MatrixN, Scalar};
+use crate::base::dimension::{DimMin, DimNameAdd, DimNameSum, U1};
+use crate::base::{Const, DefaultAllocator, Matrix2, Matrix3, Matrix4, MatrixN, Scalar};
 
 use crate::geometry::{
     AbstractRotation, Isometry, Rotation, Rotation2, Rotation3, Similarity, SuperTCategoryOf,
@@ -27,11 +27,11 @@ use crate::geometry::{
 
 */
 
-impl<N1, N2, D: DimName> SubsetOf<Rotation<N2, D>> for Rotation<N1, D>
+impl<N1, N2, const D: usize> SubsetOf<Rotation<N2, D>> for Rotation<N1, D>
 where
     N1: RealField,
     N2: RealField + SupersetOf<N1>,
-    DefaultAllocator: Allocator<N1, D, D> + Allocator<N2, D, D>,
+    // DefaultAllocator: Allocator<N1, D, D> + Allocator<N2, D, D>,
 {
     #[inline]
     fn to_superset(&self) -> Rotation<N2, D> {
@@ -120,113 +120,112 @@ where
     }
 }
 
-impl<N1, N2, D: DimName, R> SubsetOf<Isometry<N2, D, R>> for Rotation<N1, D>
+impl<N1, N2, R, const D: usize> SubsetOf<Isometry<N2, R, D>> for Rotation<N1, D>
 where
     N1: RealField,
     N2: RealField + SupersetOf<N1>,
     R: AbstractRotation<N2, D> + SupersetOf<Self>,
-    DefaultAllocator: Allocator<N1, D, D> + Allocator<N2, D>,
+    // DefaultAllocator: Allocator<N1, D, D> + Allocator<N2, D>,
 {
     #[inline]
-    fn to_superset(&self) -> Isometry<N2, D, R> {
+    fn to_superset(&self) -> Isometry<N2, R, D> {
         Isometry::from_parts(Translation::identity(), crate::convert_ref(self))
     }
 
     #[inline]
-    fn is_in_subset(iso: &Isometry<N2, D, R>) -> bool {
+    fn is_in_subset(iso: &Isometry<N2, R, D>) -> bool {
         iso.translation.vector.is_zero()
     }
 
     #[inline]
-    fn from_superset_unchecked(iso: &Isometry<N2, D, R>) -> Self {
+    fn from_superset_unchecked(iso: &Isometry<N2, R, D>) -> Self {
         crate::convert_ref_unchecked(&iso.rotation)
     }
 }
 
-impl<N1, N2, D: DimName, R> SubsetOf<Similarity<N2, D, R>> for Rotation<N1, D>
+impl<N1, N2, R, const D: usize> SubsetOf<Similarity<N2, R, D>> for Rotation<N1, D>
 where
     N1: RealField,
     N2: RealField + SupersetOf<N1>,
     R: AbstractRotation<N2, D> + SupersetOf<Self>,
-    DefaultAllocator: Allocator<N1, D, D> + Allocator<N2, D>,
+    // DefaultAllocator: Allocator<N1, D, D> + Allocator<N2, D>,
 {
     #[inline]
-    fn to_superset(&self) -> Similarity<N2, D, R> {
+    fn to_superset(&self) -> Similarity<N2, R, D> {
         Similarity::from_parts(Translation::identity(), crate::convert_ref(self), N2::one())
     }
 
     #[inline]
-    fn is_in_subset(sim: &Similarity<N2, D, R>) -> bool {
+    fn is_in_subset(sim: &Similarity<N2, R, D>) -> bool {
         sim.isometry.translation.vector.is_zero() && sim.scaling() == N2::one()
     }
 
     #[inline]
-    fn from_superset_unchecked(sim: &Similarity<N2, D, R>) -> Self {
+    fn from_superset_unchecked(sim: &Similarity<N2, R, D>) -> Self {
         crate::convert_ref_unchecked(&sim.isometry.rotation)
     }
 }
 
-impl<N1, N2, D, C> SubsetOf<Transform<N2, D, C>> for Rotation<N1, D>
+impl<N1, N2, C, const D: usize> SubsetOf<Transform<N2, C, D>> for Rotation<N1, D>
 where
     N1: RealField,
     N2: RealField + SupersetOf<N1>,
     C: SuperTCategoryOf<TAffine>,
-    D: DimNameAdd<U1> + DimMin<D, Output = D>, // needed by .is_special_orthogonal()
-    DefaultAllocator: Allocator<N1, D, D>
-        + Allocator<N2, D, D>
-        + Allocator<N1, DimNameSum<D, U1>, DimNameSum<D, U1>>
-        + Allocator<N2, DimNameSum<D, U1>, DimNameSum<D, U1>>
-        + Allocator<(usize, usize), D>,
+    Const<D>: DimNameAdd<U1> + DimMin<Const<D>, Output = Const<D>>, // needed by .is_special_orthogonal()
+    DefaultAllocator: Allocator<N1, DimNameSum<Const<D>, U1>, DimNameSum<Const<D>, U1>>
+        + Allocator<N2, DimNameSum<Const<D>, U1>, DimNameSum<Const<D>, U1>>,
+    // + Allocator<(usize, usize), D>,
+    // Allocator<N1, D, D>
+    //     + Allocator<N2, D, D>
 {
     // needed by .is_special_orthogonal()
     #[inline]
-    fn to_superset(&self) -> Transform<N2, D, C> {
+    fn to_superset(&self) -> Transform<N2, C, D> {
         Transform::from_matrix_unchecked(self.to_homogeneous().to_superset())
     }
 
     #[inline]
-    fn is_in_subset(t: &Transform<N2, D, C>) -> bool {
+    fn is_in_subset(t: &Transform<N2, C, D>) -> bool {
         <Self as SubsetOf<_>>::is_in_subset(t.matrix())
     }
 
     #[inline]
-    fn from_superset_unchecked(t: &Transform<N2, D, C>) -> Self {
+    fn from_superset_unchecked(t: &Transform<N2, C, D>) -> Self {
         Self::from_superset_unchecked(t.matrix())
     }
 }
 
-impl<N1, N2, D> SubsetOf<MatrixN<N2, DimNameSum<D, U1>>> for Rotation<N1, D>
+impl<N1, N2, const D: usize> SubsetOf<MatrixN<N2, DimNameSum<Const<D>, U1>>> for Rotation<N1, D>
 where
     N1: RealField,
     N2: RealField + SupersetOf<N1>,
-    D: DimNameAdd<U1> + DimMin<D, Output = D>, // needed by .is_special_orthogonal()
-    DefaultAllocator: Allocator<N1, D, D>
-        + Allocator<N2, D, D>
-        + Allocator<N1, DimNameSum<D, U1>, DimNameSum<D, U1>>
-        + Allocator<N2, DimNameSum<D, U1>, DimNameSum<D, U1>>
-        + Allocator<(usize, usize), D>,
+    Const<D>: DimNameAdd<U1> + DimMin<Const<D>, Output = Const<D>>, // needed by .is_special_orthogonal()
+    DefaultAllocator: Allocator<N1, DimNameSum<Const<D>, U1>, DimNameSum<Const<D>, U1>>
+        + Allocator<N2, DimNameSum<Const<D>, U1>, DimNameSum<Const<D>, U1>>, // + Allocator<(usize, usize), D>,
+                                                                             // + Allocator<N1, D, D>
+                                                                             // + Allocator<N2, D, D>
 {
     // needed by .is_special_orthogonal()
     #[inline]
-    fn to_superset(&self) -> MatrixN<N2, DimNameSum<D, U1>> {
+    fn to_superset(&self) -> MatrixN<N2, DimNameSum<Const<D>, U1>> {
         self.to_homogeneous().to_superset()
     }
 
     #[inline]
-    fn is_in_subset(m: &MatrixN<N2, DimNameSum<D, U1>>) -> bool {
+    fn is_in_subset(m: &MatrixN<N2, DimNameSum<Const<D>, U1>>) -> bool {
         let rot = m.fixed_slice::<D, D>(0, 0);
-        let bottom = m.fixed_slice::<U1, D>(D::dim(), 0);
+        let bottom = m.fixed_slice::<U1, D>(D, 0);
 
         // Scalar types agree.
         m.iter().all(|e| SupersetOf::<N1>::is_in_subset(e)) &&
         // The block part is a rotation.
         rot.is_special_orthogonal(N2::default_epsilon() * crate::convert(100.0)) &&
         // The bottom row is (0, 0, ..., 1)
-        bottom.iter().all(|e| e.is_zero()) && m[(D::dim(), D::dim())] == N2::one()
+        bottom.iter().all(|e| e.is_zero()) && m[(D, D)] == N2::one()
     }
 
     #[inline]
-    fn from_superset_unchecked(m: &MatrixN<N2, DimNameSum<D, U1>>) -> Self {
+    fn from_superset_unchecked(m: &MatrixN<N2, DimNameSum<Const<D>, U1>>) -> Self {
         let r = m.fixed_slice::<D, D>(0, 0);
         Self::from_matrix_unchecked(crate::convert_unchecked(r.into_owned()))
     }
@@ -260,12 +259,12 @@ impl<N: RealField> From<Rotation3<N>> for Matrix3<N> {
     }
 }
 
-impl<N: Scalar + PrimitiveSimdValue, D: DimName> From<[Rotation<N::Element, D>; 2]>
+impl<N: Scalar + PrimitiveSimdValue, const D: usize> From<[Rotation<N::Element, D>; 2]>
     for Rotation<N, D>
 where
     N: From<[<N as SimdValue>::Element; 2]>,
     N::Element: Scalar + Copy,
-    DefaultAllocator: Allocator<N, D, D> + Allocator<N::Element, D, D>,
+    // DefaultAllocator: Allocator<N, D, D> + Allocator<N::Element, D, D>,
 {
     #[inline]
     fn from(arr: [Rotation<N::Element, D>; 2]) -> Self {
@@ -276,12 +275,12 @@ where
     }
 }
 
-impl<N: Scalar + PrimitiveSimdValue, D: DimName> From<[Rotation<N::Element, D>; 4]>
+impl<N: Scalar + PrimitiveSimdValue, const D: usize> From<[Rotation<N::Element, D>; 4]>
     for Rotation<N, D>
 where
     N: From<[<N as SimdValue>::Element; 4]>,
     N::Element: Scalar + Copy,
-    DefaultAllocator: Allocator<N, D, D> + Allocator<N::Element, D, D>,
+    // DefaultAllocator: Allocator<N, D, D> + Allocator<N::Element, D, D>,
 {
     #[inline]
     fn from(arr: [Rotation<N::Element, D>; 4]) -> Self {
@@ -294,12 +293,12 @@ where
     }
 }
 
-impl<N: Scalar + PrimitiveSimdValue, D: DimName> From<[Rotation<N::Element, D>; 8]>
+impl<N: Scalar + PrimitiveSimdValue, const D: usize> From<[Rotation<N::Element, D>; 8]>
     for Rotation<N, D>
 where
     N: From<[<N as SimdValue>::Element; 8]>,
     N::Element: Scalar + Copy,
-    DefaultAllocator: Allocator<N, D, D> + Allocator<N::Element, D, D>,
+    // DefaultAllocator: Allocator<N, D, D> + Allocator<N::Element, D, D>,
 {
     #[inline]
     fn from(arr: [Rotation<N::Element, D>; 8]) -> Self {
@@ -316,12 +315,12 @@ where
     }
 }
 
-impl<N: Scalar + PrimitiveSimdValue, D: DimName> From<[Rotation<N::Element, D>; 16]>
+impl<N: Scalar + PrimitiveSimdValue, const D: usize> From<[Rotation<N::Element, D>; 16]>
     for Rotation<N, D>
 where
     N: From<[<N as SimdValue>::Element; 16]>,
     N::Element: Scalar + Copy,
-    DefaultAllocator: Allocator<N, D, D> + Allocator<N::Element, D, D>,
+    // DefaultAllocator: Allocator<N, D, D> + Allocator<N::Element, D, D>,
 {
     #[inline]
     fn from(arr: [Rotation<N::Element, D>; 16]) -> Self {
diff --git a/src/geometry/rotation_simba.rs b/src/geometry/rotation_simba.rs
index cb064a81..319fcc3c 100755
--- a/src/geometry/rotation_simba.rs
+++ b/src/geometry/rotation_simba.rs
@@ -1,17 +1,14 @@
 use simba::simd::SimdValue;
 
-use crate::base::allocator::Allocator;
-use crate::base::dimension::DimName;
-use crate::base::{DefaultAllocator, MatrixN, Scalar};
+use crate::base::{MatrixN, Scalar};
 
 use crate::geometry::Rotation;
 
-impl<N, D> SimdValue for Rotation<N, D>
+impl<N, const D: usize> SimdValue for Rotation<N, D>
 where
     N: Scalar + SimdValue,
-    D: DimName,
     N::Element: Scalar,
-    DefaultAllocator: Allocator<N, D, D> + Allocator<N::Element, D, D>,
+    // DefaultAllocator: Allocator<N, D, D> + Allocator<N::Element, D, D>,
 {
     type Element = Rotation<N::Element, D>;
     type SimdBool = N::SimdBool;
diff --git a/src/geometry/similarity.rs b/src/geometry/similarity.rs
index fab54759..81203fb9 100755
--- a/src/geometry/similarity.rs
+++ b/src/geometry/similarity.rs
@@ -16,9 +16,9 @@ use simba::scalar::{RealField, SubsetOf};
 use simba::simd::SimdRealField;
 
 use crate::base::allocator::Allocator;
-use crate::base::dimension::{DimName, DimNameAdd, DimNameSum, U1};
+use crate::base::dimension::{DimNameAdd, DimNameSum, U1};
 use crate::base::storage::Owned;
-use crate::base::{DefaultAllocator, MatrixN, Scalar, VectorN};
+use crate::base::{CVectorN, Const, DefaultAllocator, MatrixN, Scalar};
 use crate::geometry::{AbstractRotation, Isometry, Point, Translation};
 
 /// A similarity, i.e., an uniform scaling, followed by a rotation, followed by a translation.
@@ -39,20 +39,20 @@ use crate::geometry::{AbstractRotation, Isometry, Point, Translation};
                        DefaultAllocator: Allocator<N, D>,
                        Owned<N, D>: Deserialize<'de>"))
 )]
-pub struct Similarity<N: Scalar, D: DimName, R>
-where
-    DefaultAllocator: Allocator<N, D>,
+pub struct Similarity<N: Scalar, R, const D: usize>
+// where
+//     DefaultAllocator: Allocator<N, D>,
 {
     /// The part of this similarity that does not include the scaling factor.
-    pub isometry: Isometry<N, D, R>,
+    pub isometry: Isometry<N, R, D>,
     scaling: N,
 }
 
 #[cfg(feature = "abomonation-serialize")]
-impl<N: Scalar, D: DimName, R> Abomonation for Similarity<N, D, R>
+impl<N: Scalar, R, const D: usize> Abomonation for Similarity<N, R, D>
 where
-    Isometry<N, D, R>: Abomonation,
-    DefaultAllocator: Allocator<N, D>,
+    Isometry<N, R, D>: Abomonation,
+    // DefaultAllocator: Allocator<N, D>,
 {
     unsafe fn entomb<W: Write>(&self, writer: &mut W) -> IOResult<()> {
         self.isometry.entomb(writer)
@@ -67,11 +67,10 @@ where
     }
 }
 
-impl<N: Scalar + hash::Hash, D: DimName + hash::Hash, R: hash::Hash> hash::Hash
-    for Similarity<N, D, R>
+impl<N: Scalar + hash::Hash, R: hash::Hash, const D: usize> hash::Hash for Similarity<N, R, D>
 where
-    DefaultAllocator: Allocator<N, D>,
-    Owned<N, D>: hash::Hash,
+    // DefaultAllocator: Allocator<N, D>,
+    Owned<N, Const<D>>: hash::Hash,
 {
     fn hash<H: hash::Hasher>(&self, state: &mut H) {
         self.isometry.hash(state);
@@ -79,17 +78,18 @@ where
     }
 }
 
-impl<N: Scalar + Copy + Zero, D: DimName + Copy, R: AbstractRotation<N, D> + Copy> Copy
-    for Similarity<N, D, R>
+impl<N: Scalar + Copy + Zero, R: AbstractRotation<N, D> + Copy, const D: usize> Copy
+    for Similarity<N, R, D>
 where
-    DefaultAllocator: Allocator<N, D>,
-    Owned<N, D>: Copy,
+    // DefaultAllocator: Allocator<N, D>,
+    Owned<N, Const<D>>: Copy,
 {
 }
 
-impl<N: Scalar + Zero, D: DimName, R: AbstractRotation<N, D> + Clone> Clone for Similarity<N, D, R>
-where
-    DefaultAllocator: Allocator<N, D>,
+impl<N: Scalar + Zero, R: AbstractRotation<N, D> + Clone, const D: usize> Clone
+    for Similarity<N, R, D>
+// where
+//     DefaultAllocator: Allocator<N, D>,
 {
     #[inline]
     fn clone(&self) -> Self {
@@ -97,10 +97,10 @@ where
     }
 }
 
-impl<N: Scalar + Zero, D: DimName, R> Similarity<N, D, R>
+impl<N: Scalar + Zero, R, const D: usize> Similarity<N, R, D>
 where
     R: AbstractRotation<N, D>,
-    DefaultAllocator: Allocator<N, D>,
+    // DefaultAllocator: Allocator<N, D>,
 {
     /// Creates a new similarity from its rotational and translational parts.
     #[inline]
@@ -110,7 +110,7 @@ where
 
     /// Creates a new similarity from its rotational and translational parts.
     #[inline]
-    pub fn from_isometry(isometry: Isometry<N, D, R>, scaling: N) -> Self {
+    pub fn from_isometry(isometry: Isometry<N, R, D>, scaling: N) -> Self {
         assert!(!scaling.is_zero(), "The scaling factor must not be zero.");
 
         Self { isometry, scaling }
@@ -128,9 +128,9 @@ where
     }
 }
 
-impl<N: Scalar, D: DimName, R> Similarity<N, D, R>
-where
-    DefaultAllocator: Allocator<N, D>,
+impl<N: Scalar, R, const D: usize> Similarity<N, R, D>
+// where
+//     DefaultAllocator: Allocator<N, D>,
 {
     /// The scaling factor of this similarity transformation.
     #[inline]
@@ -139,11 +139,11 @@ where
     }
 }
 
-impl<N: SimdRealField, D: DimName, R> Similarity<N, D, R>
+impl<N: SimdRealField, R, const D: usize> Similarity<N, R, D>
 where
     N::Element: SimdRealField,
     R: AbstractRotation<N, D>,
-    DefaultAllocator: Allocator<N, D>,
+    // DefaultAllocator: Allocator<N, D>,
 {
     /// Creates a new similarity that applies only a scaling factor.
     #[inline]
@@ -282,7 +282,7 @@ where
     /// assert_relative_eq!(transformed_vector, Vector3::new(18.0, 15.0, -12.0), epsilon = 1.0e-5);
     /// ```
     #[inline]
-    pub fn transform_vector(&self, v: &VectorN<N, D>) -> VectorN<N, D> {
+    pub fn transform_vector(&self, v: &CVectorN<N, D>) -> CVectorN<N, D> {
         self * v
     }
 
@@ -322,7 +322,7 @@ where
     /// assert_relative_eq!(transformed_vector, Vector3::new(-3.0, 2.5, 2.0), epsilon = 1.0e-5);
     /// ```
     #[inline]
-    pub fn inverse_transform_vector(&self, v: &VectorN<N, D>) -> VectorN<N, D> {
+    pub fn inverse_transform_vector(&self, v: &CVectorN<N, D>) -> CVectorN<N, D> {
         self.isometry.inverse_transform_vector(v) / self.scaling()
     }
 }
@@ -331,17 +331,17 @@ where
 // and makes it harder to use it, e.g., for Transform × Isometry implementation.
 // This is OK since all constructors of the isometry enforce the Rotation bound already (and
 // explicit struct construction is prevented by the private scaling factor).
-impl<N: SimdRealField, D: DimName, R> Similarity<N, D, R>
-where
-    DefaultAllocator: Allocator<N, D>,
+impl<N: SimdRealField, R, const D: usize> Similarity<N, R, D>
+// where
+//     DefaultAllocator: Allocator<N, D>,
 {
     /// Converts this similarity into its equivalent homogeneous transformation matrix.
     #[inline]
-    pub fn to_homogeneous(&self) -> MatrixN<N, DimNameSum<D, U1>>
+    pub fn to_homogeneous(&self) -> MatrixN<N, DimNameSum<Const<D>, U1>>
     where
-        D: DimNameAdd<U1>,
-        R: SubsetOf<MatrixN<N, DimNameSum<D, U1>>>,
-        DefaultAllocator: Allocator<N, DimNameSum<D, U1>, DimNameSum<D, U1>>,
+        Const<D>: DimNameAdd<U1>,
+        R: SubsetOf<MatrixN<N, DimNameSum<Const<D>, U1>>>,
+        DefaultAllocator: Allocator<N, DimNameSum<Const<D>, U1>, DimNameSum<Const<D>, U1>>,
     {
         let mut res = self.isometry.to_homogeneous();
 
@@ -353,17 +353,15 @@ where
     }
 }
 
-impl<N: SimdRealField, D: DimName, R> Eq for Similarity<N, D, R>
-where
-    R: AbstractRotation<N, D> + Eq,
-    DefaultAllocator: Allocator<N, D>,
+impl<N: SimdRealField, R, const D: usize> Eq for Similarity<N, R, D> where
+    R: AbstractRotation<N, D> + Eq // DefaultAllocator: Allocator<N, D>,
 {
 }
 
-impl<N: SimdRealField, D: DimName, R> PartialEq for Similarity<N, D, R>
+impl<N: SimdRealField, R, const D: usize> PartialEq for Similarity<N, R, D>
 where
     R: AbstractRotation<N, D> + PartialEq,
-    DefaultAllocator: Allocator<N, D>,
+    // DefaultAllocator: Allocator<N, D>,
 {
     #[inline]
     fn eq(&self, right: &Self) -> bool {
@@ -371,10 +369,10 @@ where
     }
 }
 
-impl<N: RealField, D: DimName, R> AbsDiffEq for Similarity<N, D, R>
+impl<N: RealField, R, const D: usize> AbsDiffEq for Similarity<N, R, D>
 where
     R: AbstractRotation<N, D> + AbsDiffEq<Epsilon = N::Epsilon>,
-    DefaultAllocator: Allocator<N, D>,
+    // DefaultAllocator: Allocator<N, D>,
     N::Epsilon: Copy,
 {
     type Epsilon = N::Epsilon;
@@ -391,10 +389,10 @@ where
     }
 }
 
-impl<N: RealField, D: DimName, R> RelativeEq for Similarity<N, D, R>
+impl<N: RealField, R, const D: usize> RelativeEq for Similarity<N, R, D>
 where
     R: AbstractRotation<N, D> + RelativeEq<Epsilon = N::Epsilon>,
-    DefaultAllocator: Allocator<N, D>,
+    // DefaultAllocator: Allocator<N, D>,
     N::Epsilon: Copy,
 {
     #[inline]
@@ -417,10 +415,9 @@ where
     }
 }
 
-impl<N: RealField, D: DimName, R> UlpsEq for Similarity<N, D, R>
+impl<N: RealField, R, const D: usize> UlpsEq for Similarity<N, R, D>
 where
     R: AbstractRotation<N, D> + UlpsEq<Epsilon = N::Epsilon>,
-    DefaultAllocator: Allocator<N, D>,
     N::Epsilon: Copy,
 {
     #[inline]
@@ -440,11 +437,11 @@ where
  * Display
  *
  */
-impl<N, D: DimName, R> fmt::Display for Similarity<N, D, R>
+impl<N, R, const D: usize> fmt::Display for Similarity<N, R, D>
 where
     N: RealField + fmt::Display,
     R: AbstractRotation<N, D> + fmt::Display,
-    DefaultAllocator: Allocator<N, D> + Allocator<usize, D>,
+    // DefaultAllocator: Allocator<N, D> + Allocator<usize, D>,
 {
     fn fmt(&self, f: &mut fmt::Formatter) -> fmt::Result {
         let precision = f.precision().unwrap_or(3);
diff --git a/src/geometry/similarity_alias.rs b/src/geometry/similarity_alias.rs
index c2c887ac..9b397bbd 100644
--- a/src/geometry/similarity_alias.rs
+++ b/src/geometry/similarity_alias.rs
@@ -1,15 +1,13 @@
-use crate::base::dimension::{U2, U3};
-
 use crate::geometry::{Rotation2, Rotation3, Similarity, UnitComplex, UnitQuaternion};
 
 /// A 2-dimensional similarity.
-pub type Similarity2<N> = Similarity<N, U2, UnitComplex<N>>;
+pub type Similarity2<N> = Similarity<N, UnitComplex<N>, 2>;
 
 /// A 3-dimensional similarity.
-pub type Similarity3<N> = Similarity<N, U3, UnitQuaternion<N>>;
+pub type Similarity3<N> = Similarity<N, UnitQuaternion<N>, 3>;
 
 /// A 2-dimensional similarity using a rotation matrix for its rotation part.
-pub type SimilarityMatrix2<N> = Similarity<N, U2, Rotation2<N>>;
+pub type SimilarityMatrix2<N> = Similarity<N, Rotation2<N>, 2>;
 
 /// A 3-dimensional similarity using a rotation matrix for its rotation part.
-pub type SimilarityMatrix3<N> = Similarity<N, U3, Rotation3<N>>;
+pub type SimilarityMatrix3<N> = Similarity<N, Rotation3<N>, 3>;
diff --git a/src/geometry/similarity_construction.rs b/src/geometry/similarity_construction.rs
index 0c814534..91e4c228 100644
--- a/src/geometry/similarity_construction.rs
+++ b/src/geometry/similarity_construction.rs
@@ -13,20 +13,18 @@ use rand::{
 use simba::scalar::SupersetOf;
 use simba::simd::SimdRealField;
 
-use crate::base::allocator::Allocator;
-use crate::base::dimension::{DimName, U2, U3};
-use crate::base::{DefaultAllocator, Vector2, Vector3};
+use crate::base::{Vector2, Vector3};
 
 use crate::{
     AbstractRotation, Isometry, Point, Point3, Rotation2, Rotation3, Scalar, Similarity,
     Translation, UnitComplex, UnitQuaternion,
 };
 
-impl<N: SimdRealField, D: DimName, R> Similarity<N, D, R>
+impl<N: SimdRealField, R, const D: usize> Similarity<N, R, D>
 where
     N::Element: SimdRealField,
     R: AbstractRotation<N, D>,
-    DefaultAllocator: Allocator<N, D>,
+    // DefaultAllocator: Allocator<N, D>,
 {
     /// Creates a new identity similarity.
     ///
@@ -49,11 +47,11 @@ where
     }
 }
 
-impl<N: SimdRealField, D: DimName, R> One for Similarity<N, D, R>
+impl<N: SimdRealField, R, const D: usize> One for Similarity<N, R, D>
 where
     N::Element: SimdRealField,
     R: AbstractRotation<N, D>,
-    DefaultAllocator: Allocator<N, D>,
+    // DefaultAllocator: Allocator<N, D>,
 {
     /// Creates a new identity similarity.
     #[inline]
@@ -63,15 +61,15 @@ where
 }
 
 #[cfg(feature = "rand-no-std")]
-impl<N: crate::RealField, D: DimName, R> Distribution<Similarity<N, D, R>> for Standard
+impl<N: crate::RealField, R, const D: usize> Distribution<Similarity<N, R, D>> for Standard
 where
     R: AbstractRotation<N, D>,
-    DefaultAllocator: Allocator<N, D>,
+    // DefaultAllocator: Allocator<N, D>,
     Standard: Distribution<N> + Distribution<R>,
 {
     /// Generate an arbitrary random variate for testing purposes.
     #[inline]
-    fn sample<'a, G: Rng + ?Sized>(&self, rng: &mut G) -> Similarity<N, D, R> {
+    fn sample<'a, G: Rng + ?Sized>(&self, rng: &mut G) -> Similarity<N, R, D> {
         let mut s = rng.gen();
         while relative_eq!(s, N::zero()) {
             s = rng.gen()
@@ -81,11 +79,11 @@ where
     }
 }
 
-impl<N: SimdRealField, D: DimName, R> Similarity<N, D, R>
+impl<N: SimdRealField, R, const D: usize> Similarity<N, R, D>
 where
     N::Element: SimdRealField,
     R: AbstractRotation<N, D>,
-    DefaultAllocator: Allocator<N, D>,
+    // DefaultAllocator: Allocator<N, D>,
 {
     /// The similarity that applies the scaling factor `scaling`, followed by the rotation `r` with
     /// its axis passing through the point `p`.
@@ -110,12 +108,12 @@ where
 }
 
 #[cfg(feature = "arbitrary")]
-impl<N, D: DimName, R> Arbitrary for Similarity<N, D, R>
+impl<N, R, const D: usize> Arbitrary for Similarity<N, R, D>
 where
     N: crate::RealField + Arbitrary + Send,
     N::Element: crate::RealField,
     R: AbstractRotation<N, D> + Arbitrary + Send,
-    DefaultAllocator: Allocator<N, D>,
+    // DefaultAllocator: Allocator<N, D>,
     Owned<N, D>: Send,
 {
     #[inline]
@@ -136,7 +134,7 @@ where
  */
 
 // 2D similarity.
-impl<N: SimdRealField> Similarity<N, U2, Rotation2<N>>
+impl<N: SimdRealField> Similarity<N, Rotation2<N>, 2>
 where
     N::Element: SimdRealField,
 {
@@ -170,15 +168,15 @@ where
     /// let sim2 = sim.cast::<f32>();
     /// assert_eq!(sim2, SimilarityMatrix2::<f32>::identity());
     /// ```
-    pub fn cast<To: Scalar>(self) -> Similarity<To, U2, Rotation2<To>>
+    pub fn cast<To: Scalar>(self) -> Similarity<To, Rotation2<To>, 2>
     where
-        Similarity<To, U2, Rotation2<To>>: SupersetOf<Self>,
+        Similarity<To, Rotation2<To>, 2>: SupersetOf<Self>,
     {
         crate::convert(self)
     }
 }
 
-impl<N: SimdRealField> Similarity<N, U2, UnitComplex<N>>
+impl<N: SimdRealField> Similarity<N, UnitComplex<N>, 2>
 where
     N::Element: SimdRealField,
 {
@@ -212,9 +210,9 @@ where
     /// let sim2 = sim.cast::<f32>();
     /// assert_eq!(sim2, Similarity2::<f32>::identity());
     /// ```
-    pub fn cast<To: Scalar>(self) -> Similarity<To, U2, UnitComplex<To>>
+    pub fn cast<To: Scalar>(self) -> Similarity<To, UnitComplex<To>, 2>
     where
-        Similarity<To, U2, UnitComplex<To>>: SupersetOf<Self>,
+        Similarity<To, UnitComplex<To>, 2>: SupersetOf<Self>,
     {
         crate::convert(self)
     }
@@ -223,7 +221,7 @@ where
 // 3D rotation.
 macro_rules! similarity_construction_impl(
     ($Rot: ident) => {
-        impl<N: SimdRealField> Similarity<N, U3, $Rot<N>>
+        impl<N: SimdRealField> Similarity<N, $Rot<N>, 3>
         where N::Element: SimdRealField {
             /// Creates a new similarity from a translation, rotation axis-angle, and scaling
             /// factor.
@@ -253,7 +251,7 @@ macro_rules! similarity_construction_impl(
             #[inline]
             pub fn new(translation: Vector3<N>, axisangle: Vector3<N>, scaling: N) -> Self
             {
-                Self::from_isometry(Isometry::<_, U3, $Rot<N>>::new(translation, axisangle), scaling)
+                Self::from_isometry(Isometry::<_, $Rot<N>, 3>::new(translation, axisangle), scaling)
             }
 
             /// Cast the components of `self` to another type.
@@ -265,9 +263,9 @@ macro_rules! similarity_construction_impl(
             /// let sim2 = sim.cast::<f32>();
             /// assert_eq!(sim2, Similarity3::<f32>::identity());
             /// ```
-            pub fn cast<To: Scalar>(self) -> Similarity<To, U3, $Rot<To>>
+            pub fn cast<To: Scalar>(self) -> Similarity<To, $Rot<To>, 3>
             where
-                Similarity<To, U3, $Rot<To>>: SupersetOf<Self>,
+                Similarity<To, $Rot<To>, 3>: SupersetOf<Self>,
             {
                 crate::convert(self)
             }
@@ -306,20 +304,20 @@ macro_rules! similarity_construction_impl(
             /// ```
             #[inline]
             pub fn face_towards(eye:    &Point3<N>,
-                                      target: &Point3<N>,
-                                      up:     &Vector3<N>,
-                                      scaling: N)
-                                      -> Self {
-                Self::from_isometry(Isometry::<_, U3, $Rot<N>>::face_towards(eye, target, up), scaling)
+                                target: &Point3<N>,
+                                up:     &Vector3<N>,
+                                scaling: N)
+                                -> Self {
+                Self::from_isometry(Isometry::<_, $Rot<N>, 3>::face_towards(eye, target, up), scaling)
             }
 
             /// Deprecated: Use [SimilarityMatrix3::face_towards] instead.
             #[deprecated(note="renamed to `face_towards`")]
             pub fn new_observer_frames(eye:    &Point3<N>,
-                                      target: &Point3<N>,
-                                      up:     &Vector3<N>,
-                                      scaling: N)
-                                      -> Self {
+                                       target: &Point3<N>,
+                                       up:     &Vector3<N>,
+                                       scaling: N)
+                                       -> Self {
                 Self::face_towards(eye, target, up, scaling)
             }
 
@@ -358,7 +356,7 @@ macro_rules! similarity_construction_impl(
                               up:      &Vector3<N>,
                               scaling: N)
                               -> Self {
-                Self::from_isometry(Isometry::<_, U3, $Rot<N>>::look_at_rh(eye, target, up), scaling)
+                Self::from_isometry(Isometry::<_, $Rot<N>, 3>::look_at_rh(eye, target, up), scaling)
             }
 
             /// Builds a left-handed look-at view matrix including a scaling factor.
@@ -396,7 +394,7 @@ macro_rules! similarity_construction_impl(
                               up:      &Vector3<N>,
                               scaling: N)
                               -> Self {
-                Self::from_isometry(Isometry::<_, _, $Rot<N>>::look_at_lh(eye, target, up), scaling)
+                Self::from_isometry(Isometry::<_, $Rot<N>, _>::look_at_lh(eye, target, up), scaling)
             }
         }
     }
diff --git a/src/geometry/similarity_conversion.rs b/src/geometry/similarity_conversion.rs
index abcd7187..723d27dd 100644
--- a/src/geometry/similarity_conversion.rs
+++ b/src/geometry/similarity_conversion.rs
@@ -4,8 +4,8 @@ use simba::scalar::{RealField, SubsetOf, SupersetOf};
 use simba::simd::{PrimitiveSimdValue, SimdRealField, SimdValue};
 
 use crate::base::allocator::Allocator;
-use crate::base::dimension::{DimMin, DimName, DimNameAdd, DimNameSum, U1};
-use crate::base::{DefaultAllocator, MatrixN, Scalar};
+use crate::base::dimension::{DimMin, DimNameAdd, DimNameSum, U1};
+use crate::base::{Const, DefaultAllocator, MatrixN, Scalar};
 
 use crate::geometry::{
     AbstractRotation, Isometry, Similarity, SuperTCategoryOf, TAffine, Transform, Translation,
@@ -20,27 +20,27 @@ use crate::geometry::{
  * Similarity -> Matrix (homogeneous)
  */
 
-impl<N1, N2, D: DimName, R1, R2> SubsetOf<Similarity<N2, D, R2>> for Similarity<N1, D, R1>
+impl<N1, N2, R1, R2, const D: usize> SubsetOf<Similarity<N2, R2, D>> for Similarity<N1, R1, D>
 where
     N1: RealField + SubsetOf<N2>,
     N2: RealField + SupersetOf<N1>,
     R1: AbstractRotation<N1, D> + SubsetOf<R2>,
     R2: AbstractRotation<N2, D>,
-    DefaultAllocator: Allocator<N1, D> + Allocator<N2, D>,
+    // DefaultAllocator: Allocator<N1, D> + Allocator<N2, D>,
 {
     #[inline]
-    fn to_superset(&self) -> Similarity<N2, D, R2> {
+    fn to_superset(&self) -> Similarity<N2, R2, D> {
         Similarity::from_isometry(self.isometry.to_superset(), self.scaling().to_superset())
     }
 
     #[inline]
-    fn is_in_subset(sim: &Similarity<N2, D, R2>) -> bool {
-        crate::is_convertible::<_, Isometry<N1, D, R1>>(&sim.isometry)
+    fn is_in_subset(sim: &Similarity<N2, R2, D>) -> bool {
+        crate::is_convertible::<_, Isometry<N1, R1, D>>(&sim.isometry)
             && crate::is_convertible::<_, N1>(&sim.scaling())
     }
 
     #[inline]
-    fn from_superset_unchecked(sim: &Similarity<N2, D, R2>) -> Self {
+    fn from_superset_unchecked(sim: &Similarity<N2, R2, D>) -> Self {
         Similarity::from_isometry(
             sim.isometry.to_subset_unchecked(),
             sim.scaling().to_subset_unchecked(),
@@ -48,64 +48,64 @@ where
     }
 }
 
-impl<N1, N2, D, R, C> SubsetOf<Transform<N2, D, C>> for Similarity<N1, D, R>
+impl<N1, N2, R, C, const D: usize> SubsetOf<Transform<N2, C, D>> for Similarity<N1, R, D>
 where
     N1: RealField,
     N2: RealField + SupersetOf<N1>,
     C: SuperTCategoryOf<TAffine>,
     R: AbstractRotation<N1, D>
-        + SubsetOf<MatrixN<N1, DimNameSum<D, U1>>>
-        + SubsetOf<MatrixN<N2, DimNameSum<D, U1>>>,
-    D: DimNameAdd<U1> + DimMin<D, Output = D>, // needed by .determinant()
-    DefaultAllocator: Allocator<N1, D>
-        + Allocator<N1, D, D>
-        + Allocator<N1, DimNameSum<D, U1>, DimNameSum<D, U1>>
-        + Allocator<N2, DimNameSum<D, U1>, DimNameSum<D, U1>>
-        + Allocator<(usize, usize), D>
-        + Allocator<N2, DimNameSum<D, U1>, DimNameSum<D, U1>>
-        + Allocator<N2, D, D>
-        + Allocator<N2, D>,
+        + SubsetOf<MatrixN<N1, DimNameSum<Const<D>, U1>>>
+        + SubsetOf<MatrixN<N2, DimNameSum<Const<D>, U1>>>,
+    Const<D>: DimNameAdd<U1> + DimMin<Const<D>, Output = Const<D>>, // needed by .determinant()
+    DefaultAllocator: Allocator<N1, DimNameSum<Const<D>, U1>, DimNameSum<Const<D>, U1>>
+        + Allocator<N2, DimNameSum<Const<D>, U1>, DimNameSum<Const<D>, U1>>
+        + Allocator<N2, DimNameSum<Const<D>, U1>, DimNameSum<Const<D>, U1>>,
+    // + Allocator<(usize, usize), D>
+    // + Allocator<N1, D>
+    // + Allocator<N1, D, D>
+    // + Allocator<N2, D, D>
+    // + Allocator<N2, D>,
 {
     #[inline]
-    fn to_superset(&self) -> Transform<N2, D, C> {
+    fn to_superset(&self) -> Transform<N2, C, D> {
         Transform::from_matrix_unchecked(self.to_homogeneous().to_superset())
     }
 
     #[inline]
-    fn is_in_subset(t: &Transform<N2, D, C>) -> bool {
+    fn is_in_subset(t: &Transform<N2, C, D>) -> bool {
         <Self as SubsetOf<_>>::is_in_subset(t.matrix())
     }
 
     #[inline]
-    fn from_superset_unchecked(t: &Transform<N2, D, C>) -> Self {
+    fn from_superset_unchecked(t: &Transform<N2, C, D>) -> Self {
         Self::from_superset_unchecked(t.matrix())
     }
 }
 
-impl<N1, N2, D, R> SubsetOf<MatrixN<N2, DimNameSum<D, U1>>> for Similarity<N1, D, R>
+impl<N1, N2, R, const D: usize> SubsetOf<MatrixN<N2, DimNameSum<Const<D>, U1>>>
+    for Similarity<N1, R, D>
 where
     N1: RealField,
     N2: RealField + SupersetOf<N1>,
     R: AbstractRotation<N1, D>
-        + SubsetOf<MatrixN<N1, DimNameSum<D, U1>>>
-        + SubsetOf<MatrixN<N2, DimNameSum<D, U1>>>,
-    D: DimNameAdd<U1> + DimMin<D, Output = D>, // needed by .determinant()
-    DefaultAllocator: Allocator<N1, D>
-        + Allocator<N1, D, D>
-        + Allocator<N1, DimNameSum<D, U1>, DimNameSum<D, U1>>
-        + Allocator<N2, DimNameSum<D, U1>, DimNameSum<D, U1>>
-        + Allocator<(usize, usize), D>
-        + Allocator<N2, DimNameSum<D, U1>, DimNameSum<D, U1>>
-        + Allocator<N2, D, D>
-        + Allocator<N2, D>,
+        + SubsetOf<MatrixN<N1, DimNameSum<Const<D>, U1>>>
+        + SubsetOf<MatrixN<N2, DimNameSum<Const<D>, U1>>>,
+    Const<D>: DimNameAdd<U1> + DimMin<Const<D>, Output = Const<D>>, // needed by .determinant()
+    DefaultAllocator: Allocator<N1, DimNameSum<Const<D>, U1>, DimNameSum<Const<D>, U1>>
+        + Allocator<N2, DimNameSum<Const<D>, U1>, DimNameSum<Const<D>, U1>>
+        + Allocator<N2, DimNameSum<Const<D>, U1>, DimNameSum<Const<D>, U1>>, // + Allocator<(usize, usize), D>
+                                                                             // + Allocator<N1, D>
+                                                                             // + Allocator<N1, D, D>
+                                                                             // + Allocator<N2, D, D>
+                                                                             // + Allocator<N2, D>
 {
     #[inline]
-    fn to_superset(&self) -> MatrixN<N2, DimNameSum<D, U1>> {
+    fn to_superset(&self) -> MatrixN<N2, DimNameSum<Const<D>, U1>> {
         self.to_homogeneous().to_superset()
     }
 
     #[inline]
-    fn is_in_subset(m: &MatrixN<N2, DimNameSum<D, U1>>) -> bool {
+    fn is_in_subset(m: &MatrixN<N2, DimNameSum<Const<D>, U1>>) -> bool {
         let mut rot = m.fixed_slice::<D, D>(0, 0).clone_owned();
         if rot
             .fixed_columns_mut::<U1>(0)
@@ -128,20 +128,20 @@ where
                 rot.fixed_columns_mut::<U1>(2).neg_mut();
             }
 
-            let bottom = m.fixed_slice::<U1, D>(D::dim(), 0);
+            let bottom = m.fixed_slice::<U1, D>(D, 0);
             // Scalar types agree.
             m.iter().all(|e| SupersetOf::<N1>::is_in_subset(e)) &&
             // The normalized block part is a rotation.
             // rot.is_special_orthogonal(N2::default_epsilon().sqrt()) &&
             // The bottom row is (0, 0, ..., 1)
-            bottom.iter().all(|e| e.is_zero()) && m[(D::dim(), D::dim())] == N2::one()
+            bottom.iter().all(|e| e.is_zero()) && m[(D, D)] == N2::one()
         } else {
             false
         }
     }
 
     #[inline]
-    fn from_superset_unchecked(m: &MatrixN<N2, DimNameSum<D, U1>>) -> Self {
+    fn from_superset_unchecked(m: &MatrixN<N2, DimNameSum<Const<D>, U1>>) -> Self {
         let mut mm = m.clone_owned();
         let na = mm.fixed_slice_mut::<D, U1>(0, 0).normalize_mut();
         let nb = mm.fixed_slice_mut::<D, U1>(0, 1).normalize_mut();
@@ -158,7 +158,7 @@ where
             scale = -scale;
         }
 
-        let t = m.fixed_slice::<D, U1>(0, D::dim()).into_owned();
+        let t = m.fixed_slice::<D, U1>(0, D).into_owned();
         let t = Translation {
             vector: crate::convert_unchecked(t),
         };
@@ -171,30 +171,31 @@ where
     }
 }
 
-impl<N: SimdRealField, D: DimName, R> From<Similarity<N, D, R>> for MatrixN<N, DimNameSum<D, U1>>
+impl<N: SimdRealField, R, const D: usize> From<Similarity<N, R, D>>
+    for MatrixN<N, DimNameSum<Const<D>, U1>>
 where
-    D: DimNameAdd<U1>,
-    R: SubsetOf<MatrixN<N, DimNameSum<D, U1>>>,
-    DefaultAllocator: Allocator<N, D> + Allocator<N, DimNameSum<D, U1>, DimNameSum<D, U1>>,
+    Const<D>: DimNameAdd<U1>,
+    R: SubsetOf<MatrixN<N, DimNameSum<Const<D>, U1>>>,
+    DefaultAllocator: Allocator<N, DimNameSum<Const<D>, U1>, DimNameSum<Const<D>, U1>>, // + Allocator<N, D>
 {
     #[inline]
-    fn from(sim: Similarity<N, D, R>) -> Self {
+    fn from(sim: Similarity<N, R, D>) -> Self {
         sim.to_homogeneous()
     }
 }
 
-impl<N: Scalar + Zero + PrimitiveSimdValue, D: DimName, R>
-    From<[Similarity<N::Element, D, R::Element>; 2]> for Similarity<N, D, R>
+impl<N: Scalar + Zero + PrimitiveSimdValue, R, const D: usize>
+    From<[Similarity<N::Element, R::Element, D>; 2]> for Similarity<N, R, D>
 where
     N: From<[<N as SimdValue>::Element; 2]>,
     R: SimdValue + AbstractRotation<N, D> + From<[<R as SimdValue>::Element; 2]>,
     R::Element: AbstractRotation<N::Element, D>,
     N::Element: Scalar + Zero + Copy,
     R::Element: Scalar + Zero + Copy,
-    DefaultAllocator: Allocator<N, D> + Allocator<N::Element, D>,
+    // DefaultAllocator: Allocator<N, D> + Allocator<N::Element, D>,
 {
     #[inline]
-    fn from(arr: [Similarity<N::Element, D, R::Element>; 2]) -> Self {
+    fn from(arr: [Similarity<N::Element, R::Element, D>; 2]) -> Self {
         let iso = Isometry::from([arr[0].isometry.clone(), arr[1].isometry.clone()]);
         let scale = N::from([arr[0].scaling(), arr[1].scaling()]);
 
@@ -202,18 +203,18 @@ where
     }
 }
 
-impl<N: Scalar + Zero + PrimitiveSimdValue, D: DimName, R>
-    From<[Similarity<N::Element, D, R::Element>; 4]> for Similarity<N, D, R>
+impl<N: Scalar + Zero + PrimitiveSimdValue, R, const D: usize>
+    From<[Similarity<N::Element, R::Element, D>; 4]> for Similarity<N, R, D>
 where
     N: From<[<N as SimdValue>::Element; 4]>,
     R: SimdValue + AbstractRotation<N, D> + From<[<R as SimdValue>::Element; 4]>,
     R::Element: AbstractRotation<N::Element, D>,
     N::Element: Scalar + Zero + Copy,
     R::Element: Scalar + Zero + Copy,
-    DefaultAllocator: Allocator<N, D> + Allocator<N::Element, D>,
+    // DefaultAllocator: Allocator<N, D> + Allocator<N::Element, D>,
 {
     #[inline]
-    fn from(arr: [Similarity<N::Element, D, R::Element>; 4]) -> Self {
+    fn from(arr: [Similarity<N::Element, R::Element, D>; 4]) -> Self {
         let iso = Isometry::from([
             arr[0].isometry.clone(),
             arr[1].isometry.clone(),
@@ -231,18 +232,18 @@ where
     }
 }
 
-impl<N: Scalar + Zero + PrimitiveSimdValue, D: DimName, R>
-    From<[Similarity<N::Element, D, R::Element>; 8]> for Similarity<N, D, R>
+impl<N: Scalar + Zero + PrimitiveSimdValue, R, const D: usize>
+    From<[Similarity<N::Element, R::Element, D>; 8]> for Similarity<N, R, D>
 where
     N: From<[<N as SimdValue>::Element; 8]>,
     R: SimdValue + AbstractRotation<N, D> + From<[<R as SimdValue>::Element; 8]>,
     R::Element: AbstractRotation<N::Element, D>,
     N::Element: Scalar + Zero + Copy,
     R::Element: Scalar + Zero + Copy,
-    DefaultAllocator: Allocator<N, D> + Allocator<N::Element, D>,
+    // DefaultAllocator: Allocator<N, D> + Allocator<N::Element, D>,
 {
     #[inline]
-    fn from(arr: [Similarity<N::Element, D, R::Element>; 8]) -> Self {
+    fn from(arr: [Similarity<N::Element, R::Element, D>; 8]) -> Self {
         let iso = Isometry::from([
             arr[0].isometry.clone(),
             arr[1].isometry.clone(),
@@ -268,18 +269,18 @@ where
     }
 }
 
-impl<N: Scalar + Zero + PrimitiveSimdValue, D: DimName, R>
-    From<[Similarity<N::Element, D, R::Element>; 16]> for Similarity<N, D, R>
+impl<N: Scalar + Zero + PrimitiveSimdValue, R, const D: usize>
+    From<[Similarity<N::Element, R::Element, D>; 16]> for Similarity<N, R, D>
 where
     N: From<[<N as SimdValue>::Element; 16]>,
     R: SimdValue + AbstractRotation<N, D> + From<[<R as SimdValue>::Element; 16]>,
     R::Element: AbstractRotation<N::Element, D>,
     N::Element: Scalar + Zero + Copy,
     R::Element: Scalar + Zero + Copy,
-    DefaultAllocator: Allocator<N, D> + Allocator<N::Element, D>,
+    // DefaultAllocator: Allocator<N, D> + Allocator<N::Element, D>,
 {
     #[inline]
-    fn from(arr: [Similarity<N::Element, D, R::Element>; 16]) -> Self {
+    fn from(arr: [Similarity<N::Element, R::Element, D>; 16]) -> Self {
         let iso = Isometry::from([
             arr[0].isometry.clone(),
             arr[1].isometry.clone(),
diff --git a/src/geometry/similarity_ops.rs b/src/geometry/similarity_ops.rs
index 319d8647..4c821e21 100644
--- a/src/geometry/similarity_ops.rs
+++ b/src/geometry/similarity_ops.rs
@@ -144,7 +144,7 @@ macro_rules! similarity_binop_assign_impl_all(
 // Similarity ÷ Similarity
 similarity_binop_impl_all!(
     Mul, mul;
-    self: Similarity<N, D, R>, rhs: Similarity<N, D, R>, Output = Similarity<N, D, R>;
+    self: Similarity<N, R, D>, rhs: Similarity<N, R, D>, Output = Similarity<N, R, D>;
     [val val] => &self * &rhs;
     [ref val] =>  self * &rhs;
     [val ref] => &self *  rhs;
@@ -157,7 +157,7 @@ similarity_binop_impl_all!(
 
 similarity_binop_impl_all!(
     Div, div;
-    self: Similarity<N, D, R>, rhs: Similarity<N, D, R>, Output = Similarity<N, D, R>;
+    self: Similarity<N, R, D>, rhs: Similarity<N, R, D>, Output = Similarity<N, R, D>;
     [val val] => #[allow(clippy::suspicious_arithmetic_impl)] { self * rhs.inverse() };
     [ref val] => #[allow(clippy::suspicious_arithmetic_impl)] { self * rhs.inverse() };
     [val ref] => #[allow(clippy::suspicious_arithmetic_impl)] { self * rhs.inverse() };
@@ -167,7 +167,7 @@ similarity_binop_impl_all!(
 // Similarity ×= Translation
 similarity_binop_assign_impl_all!(
     MulAssign, mul_assign;
-    self: Similarity<N, D, R>, rhs: Translation<N, D>;
+    self: Similarity<N, R, D>, rhs: Translation<N, D>;
     [val] => *self *= &rhs;
     [ref] => {
         let shift = self.isometry.rotation.transform_vector(&rhs.vector) * self.scaling();
@@ -179,7 +179,7 @@ similarity_binop_assign_impl_all!(
 // Similarity ÷= Similarity
 similarity_binop_assign_impl_all!(
     MulAssign, mul_assign;
-    self: Similarity<N, D, R>, rhs: Similarity<N, D, R>;
+    self: Similarity<N, R, D>, rhs: Similarity<N, R, D>;
     [val] => *self *= &rhs;
     [ref] => {
         *self *= &rhs.isometry;
@@ -189,7 +189,7 @@ similarity_binop_assign_impl_all!(
 
 similarity_binop_assign_impl_all!(
     DivAssign, div_assign;
-    self: Similarity<N, D, R>, rhs: Similarity<N, D, R>;
+    self: Similarity<N, R, D>, rhs: Similarity<N, R, D>;
     [val] => *self /= &rhs;
     // TODO: don't invert explicitly.
     [ref] => #[allow(clippy::suspicious_op_assign_impl)] { *self *= rhs.inverse() };
@@ -199,7 +199,7 @@ similarity_binop_assign_impl_all!(
 // Similarity ÷= Isometry
 similarity_binop_assign_impl_all!(
     MulAssign, mul_assign;
-    self: Similarity<N, D, R>, rhs: Isometry<N, D, R>;
+    self: Similarity<N, R, D>, rhs: Isometry<N, R, D>;
     [val] => *self *= &rhs;
     [ref] => {
         let shift = self.isometry.rotation.transform_vector(&rhs.translation.vector) * self.scaling();
@@ -210,7 +210,7 @@ similarity_binop_assign_impl_all!(
 
 similarity_binop_assign_impl_all!(
     DivAssign, div_assign;
-    self: Similarity<N, D, R>, rhs: Isometry<N, D, R>;
+    self: Similarity<N, R, D>, rhs: Isometry<N, R, D>;
     [val] => *self /= &rhs;
     // TODO: don't invert explicitly.
     [ref] => #[allow(clippy::suspicious_op_assign_impl)] { *self *= rhs.inverse() };
@@ -238,7 +238,7 @@ md_assign_impl_all!(
 md_assign_impl_all!(
     MulAssign, mul_assign where N: SimdRealField for N::Element: SimdRealField;
     (U3, U3), (U3, U3) for;
-    self: Similarity<N, U3, UnitQuaternion<N>>, rhs: UnitQuaternion<N>;
+    self: Similarity<N, UnitQuaternion<N>, 3>, rhs: UnitQuaternion<N>;
     [val] => self.isometry.rotation *= rhs;
     [ref] => self.isometry.rotation *= *rhs;
 );
@@ -246,7 +246,7 @@ md_assign_impl_all!(
 md_assign_impl_all!(
     DivAssign, div_assign where N: SimdRealField for N::Element: SimdRealField;
     (U3, U3), (U3, U3) for;
-    self: Similarity<N, U3, UnitQuaternion<N>>, rhs: UnitQuaternion<N>;
+    self: Similarity<N, UnitQuaternion<N>, 3>, rhs: UnitQuaternion<N>;
     // TODO: don't invert explicitly?
     [val] => #[allow(clippy::suspicious_op_assign_impl)] { *self *= rhs.inverse() };
     [ref] => #[allow(clippy::suspicious_op_assign_impl)] { *self *= rhs.inverse() };
@@ -273,7 +273,7 @@ md_assign_impl_all!(
 // Similarity ÷ Isometry
 similarity_binop_impl_all!(
     Mul, mul;
-    self: Similarity<N, D, R>, rhs: Isometry<N, D, R>, Output = Similarity<N, D, R>;
+    self: Similarity<N, R, D>, rhs: Isometry<N, R, D>, Output = Similarity<N, R, D>;
     [val val] => &self * &rhs;
     [ref val] => self * &rhs;
     [val ref] => &self * rhs;
@@ -289,7 +289,7 @@ similarity_binop_impl_all!(
 
 similarity_binop_impl_all!(
     Div, div;
-    self: Similarity<N, D, R>, rhs: Isometry<N, D, R>, Output = Similarity<N, D, R>;
+    self: Similarity<N, R, D>, rhs: Isometry<N, R, D>, Output = Similarity<N, R, D>;
     [val val] => #[allow(clippy::suspicious_arithmetic_impl)] { self * rhs.inverse() };
     [ref val] => #[allow(clippy::suspicious_arithmetic_impl)] { self * rhs.inverse() };
     [val ref] => #[allow(clippy::suspicious_arithmetic_impl)] { self * rhs.inverse() };
@@ -300,7 +300,7 @@ similarity_binop_impl_all!(
 // Isometry ÷ Similarity
 similarity_binop_impl_all!(
     Mul, mul;
-    self: Isometry<N, D, R>, rhs: Similarity<N, D, R>, Output = Similarity<N, D, R>;
+    self: Isometry<N, R, D>, rhs: Similarity<N, R, D>, Output = Similarity<N, R, D>;
     [val val] => {
         let scaling = rhs.scaling();
         Similarity::from_isometry(self * rhs.isometry, scaling)
@@ -321,7 +321,7 @@ similarity_binop_impl_all!(
 
 similarity_binop_impl_all!(
     Div, div;
-    self: Isometry<N, D, R>, rhs: Similarity<N, D, R>, Output = Similarity<N, D, R>;
+    self: Isometry<N, R, D>, rhs: Similarity<N, R, D>, Output = Similarity<N, R, D>;
     [val val] => #[allow(clippy::suspicious_arithmetic_impl)] { self * rhs.inverse() };
     [ref val] => #[allow(clippy::suspicious_arithmetic_impl)] { self * rhs.inverse() };
     [val ref] => #[allow(clippy::suspicious_arithmetic_impl)] { self * rhs.inverse() };
@@ -331,7 +331,7 @@ similarity_binop_impl_all!(
 // Similarity × Point
 similarity_binop_impl_all!(
     Mul, mul;
-    self: Similarity<N, D, R>, right: Point<N, D>, Output = Point<N, D>;
+    self: Similarity<N, R, D>, right: Point<N, D>, Output = Point<N, D>;
     [val val] => {
         let scaling = self.scaling();
         self.isometry.translation * (self.isometry.rotation.transform_point(&right) * scaling)
@@ -347,7 +347,7 @@ similarity_binop_impl_all!(
 // Similarity × Vector
 similarity_binop_impl_all!(
     Mul, mul;
-    self: Similarity<N, D, R>, right: VectorN<N, D>, Output = VectorN<N, D>;
+    self: Similarity<N, R, D>, right: VectorN<N, D>, Output = VectorN<N, D>;
     [val val] => self.isometry.rotation.transform_vector(&right) * self.scaling();
     [ref val] => self.isometry.rotation.transform_vector(&right) * self.scaling();
     [val ref] => self.isometry.rotation.transform_vector(right) * self.scaling();
@@ -357,7 +357,7 @@ similarity_binop_impl_all!(
 // Similarity × Translation
 similarity_binop_impl_all!(
     Mul, mul;
-    self: Similarity<N, D, R>, right: Translation<N, D>, Output = Similarity<N, D, R>;
+    self: Similarity<N, R, D>, right: Translation<N, D>, Output = Similarity<N, R, D>;
     [val val] => &self * &right;
     [ref val] => self * &right;
     [val ref] => &self * right;
@@ -374,7 +374,7 @@ similarity_binop_impl_all!(
 // Translation × Similarity
 similarity_binop_impl_all!(
     Mul, mul;
-    self: Translation<N, D>, right: Similarity<N, D, R>, Output = Similarity<N, D, R>;
+    self: Translation<N, D>, right: Similarity<N, R, D>, Output = Similarity<N, R, D>;
     [val val] => {
         let scaling = right.scaling();
         Similarity::from_isometry(self * right.isometry, scaling)
@@ -506,8 +506,8 @@ similarity_from_composition_impl_all!(
 similarity_from_composition_impl_all!(
     Mul, mul;
     (U4, U1), (U3, U1);
-    self: Similarity<N, U3, UnitQuaternion<N>>, rhs: UnitQuaternion<N>,
-    Output = Similarity<N, U3, UnitQuaternion<N>>;
+    self: Similarity<N, UnitQuaternion<N>, 3>, rhs: UnitQuaternion<N>,
+    Output = Similarity<N, UnitQuaternion<N>, 3>;
     [val val] => {
         let scaling = self.scaling();
         Similarity::from_isometry(self.isometry * rhs, scaling)
@@ -524,8 +524,8 @@ similarity_from_composition_impl_all!(
 similarity_from_composition_impl_all!(
     Mul, mul;
     (U4, U1), (U3, U1);
-    self: UnitQuaternion<N>, right: Similarity<N, U3, UnitQuaternion<N>>,
-    Output = Similarity<N, U3, UnitQuaternion<N>>;
+    self: UnitQuaternion<N>, right: Similarity<N, UnitQuaternion<N>, 3>,
+    Output = Similarity<N, UnitQuaternion<N>, 3>;
     [val val] => &self * &right;
     [ref val] =>  self * &right;
     [val ref] => &self *  right;
@@ -536,8 +536,8 @@ similarity_from_composition_impl_all!(
 similarity_from_composition_impl_all!(
     Div, div;
     (U4, U1), (U3, U1);
-    self: Similarity<N, U3, UnitQuaternion<N>>, rhs: UnitQuaternion<N>,
-    Output = Similarity<N, U3, UnitQuaternion<N>>;
+    self: Similarity<N, UnitQuaternion<N>, 3>, rhs: UnitQuaternion<N>,
+    Output = Similarity<N, UnitQuaternion<N>, 3>;
     [val val] => {
         let scaling = self.scaling();
         Similarity::from_isometry(self.isometry / rhs, scaling)
@@ -554,8 +554,8 @@ similarity_from_composition_impl_all!(
 similarity_from_composition_impl_all!(
     Div, div;
     (U4, U1), (U3, U1);
-    self: UnitQuaternion<N>, right: Similarity<N, U3, UnitQuaternion<N>>,
-    Output = Similarity<N, U3, UnitQuaternion<N>>;
+    self: UnitQuaternion<N>, right: Similarity<N, UnitQuaternion<N>, 3>,
+    Output = Similarity<N, UnitQuaternion<N>, 3>;
     // TODO: don't call inverse explicitly?
     [val val] => #[allow(clippy::suspicious_arithmetic_impl)] { self * right.inverse() };
     [ref val] => #[allow(clippy::suspicious_arithmetic_impl)] { self * right.inverse() };
diff --git a/src/geometry/similarity_simba.rs b/src/geometry/similarity_simba.rs
index bf3858f7..0436130a 100755
--- a/src/geometry/similarity_simba.rs
+++ b/src/geometry/similarity_simba.rs
@@ -1,19 +1,15 @@
 use simba::simd::{SimdRealField, SimdValue};
 
-use crate::base::allocator::Allocator;
-use crate::base::dimension::DimName;
-use crate::base::DefaultAllocator;
-
 use crate::geometry::{AbstractRotation, Isometry, Similarity};
 
-impl<N: SimdRealField, D: DimName, R> SimdValue for Similarity<N, D, R>
+impl<N: SimdRealField, R, const D: usize> SimdValue for Similarity<N, R, D>
 where
     N::Element: SimdRealField,
     R: SimdValue<SimdBool = N::SimdBool> + AbstractRotation<N, D>,
     R::Element: AbstractRotation<N::Element, D>,
-    DefaultAllocator: Allocator<N, D> + Allocator<N::Element, D>,
+    // DefaultAllocator: Allocator<N, D> + Allocator<N::Element, D>,
 {
-    type Element = Similarity<N::Element, D, R::Element>;
+    type Element = Similarity<N::Element, R::Element, D>;
     type SimdBool = N::SimdBool;
 
     #[inline]
diff --git a/src/geometry/swizzle.rs b/src/geometry/swizzle.rs
index 7797e02b..e0c42eaa 100644
--- a/src/geometry/swizzle.rs
+++ b/src/geometry/swizzle.rs
@@ -1,5 +1,4 @@
-use crate::base::allocator::Allocator;
-use crate::base::{DefaultAllocator, DimName, Scalar, ToTypenum};
+use crate::base::{Const, Scalar, ToTypenum};
 use crate::geometry::{Point, Point2, Point3};
 use typenum::{self, Cmp, Greater};
 
@@ -10,7 +9,7 @@ macro_rules! impl_swizzle {
                 /// Builds a new point from components of `self`.
                 #[inline]
                 pub fn $name(&self) -> $Result<N>
-                 where D::Typenum: Cmp<typenum::$BaseDim, Output=Greater> {
+                 where <Const<D> as ToTypenum>::Typenum: Cmp<typenum::$BaseDim, Output=Greater> {
                     $Result::new($(self[$i].inlined_clone()),*)
                 }
             )*
@@ -19,10 +18,10 @@ macro_rules! impl_swizzle {
 }
 
 /// # Swizzling
-impl<N: Scalar, D> Point<N, D>
+impl<N: Scalar, const D: usize> Point<N, D>
 where
-    D: DimName + ToTypenum,
-    DefaultAllocator: Allocator<N, D>,
+    Const<D>: ToTypenum,
+    // DefaultAllocator: Allocator<N, D>,
 {
     impl_swizzle!(
         where U0: xx()  -> Point2[0, 0],
diff --git a/src/geometry/transform.rs b/src/geometry/transform.rs
index b15eb28f..15b2c939 100755
--- a/src/geometry/transform.rs
+++ b/src/geometry/transform.rs
@@ -9,9 +9,9 @@ use serde::{Deserialize, Deserializer, Serialize, Serializer};
 use simba::scalar::RealField;
 
 use crate::base::allocator::Allocator;
-use crate::base::dimension::{DimName, DimNameAdd, DimNameSum, U1};
+use crate::base::dimension::{DimNameAdd, DimNameSum, U1};
 use crate::base::storage::Owned;
-use crate::base::{DefaultAllocator, MatrixN, VectorN};
+use crate::base::{CMatrixN, CVectorN, Const, DefaultAllocator, MatrixN};
 
 use crate::geometry::Point;
 
@@ -28,10 +28,10 @@ pub trait TCategory: Any + Debug + Copy + PartialEq + Send {
 
     /// Checks that the given matrix is a valid homogeneous representation of an element of the
     /// category `Self`.
-    fn check_homogeneous_invariants<N: RealField, D: DimName>(mat: &MatrixN<N, D>) -> bool
+    fn check_homogeneous_invariants<N: RealField, const D: usize>(mat: &CMatrixN<N, D>) -> bool
     where
-        N::Epsilon: Copy,
-        DefaultAllocator: Allocator<N, D, D>;
+        N::Epsilon: Copy;
+    // DefaultAllocator: Allocator<N, D, D>;
 }
 
 /// Traits that gives the `Transform` category that is compatible with the result of the
@@ -71,10 +71,10 @@ pub enum TAffine {}
 
 impl TCategory for TGeneral {
     #[inline]
-    fn check_homogeneous_invariants<N: RealField, D: DimName>(_: &MatrixN<N, D>) -> bool
+    fn check_homogeneous_invariants<N: RealField, const D: usize>(_: &CMatrixN<N, D>) -> bool
     where
         N::Epsilon: Copy,
-        DefaultAllocator: Allocator<N, D, D>,
+        // DefaultAllocator: Allocator<N, D, D>,
     {
         true
     }
@@ -82,10 +82,10 @@ impl TCategory for TGeneral {
 
 impl TCategory for TProjective {
     #[inline]
-    fn check_homogeneous_invariants<N: RealField, D: DimName>(mat: &MatrixN<N, D>) -> bool
+    fn check_homogeneous_invariants<N: RealField, const D: usize>(mat: &CMatrixN<N, D>) -> bool
     where
         N::Epsilon: Copy,
-        DefaultAllocator: Allocator<N, D, D>,
+        // DefaultAllocator: Allocator<N, D, D>,
     {
         mat.is_invertible()
     }
@@ -98,12 +98,12 @@ impl TCategory for TAffine {
     }
 
     #[inline]
-    fn check_homogeneous_invariants<N: RealField, D: DimName>(mat: &MatrixN<N, D>) -> bool
+    fn check_homogeneous_invariants<N: RealField, const D: usize>(mat: &CMatrixN<N, D>) -> bool
     where
         N::Epsilon: Copy,
-        DefaultAllocator: Allocator<N, D, D>,
+        // DefaultAllocator: Allocator<N, D, D>,
     {
-        let last = D::dim() - 1;
+        let last = D - 1;
         mat.is_invertible()
             && mat[(last, last)] == N::one()
             && (0..last).all(|i| mat[(last, i)].is_zero())
@@ -157,33 +157,36 @@ super_tcategory_impl!(
 /// 3D transformation.
 #[repr(C)]
 #[derive(Debug)]
-pub struct Transform<N: RealField, D: DimNameAdd<U1>, C: TCategory>
+pub struct Transform<N: RealField, C: TCategory, const D: usize>
 where
-    DefaultAllocator: Allocator<N, DimNameSum<D, U1>, DimNameSum<D, U1>>,
+    Const<D>: DimNameAdd<U1>,
+    DefaultAllocator: Allocator<N, DimNameSum<Const<D>, U1>, DimNameSum<Const<D>, U1>>,
 {
-    matrix: MatrixN<N, DimNameSum<D, U1>>,
+    matrix: MatrixN<N, DimNameSum<Const<D>, U1>>,
     _phantom: PhantomData<C>,
 }
 
 // TODO
-// impl<N: RealField + hash::Hash, D: DimNameAdd<U1> + hash::Hash, C: TCategory> hash::Hash for Transform<N, D, C>
-//     where DefaultAllocator: Allocator<N, DimNameSum<D, U1>, DimNameSum<D, U1>>,
-//           Owned<N, DimNameSum<D, U1>, DimNameSum<D, U1>>: hash::Hash {
+// impl<N: RealField + hash::Hash, D: DimNameAdd<U1> + hash::Hash, C: TCategory> hash::Hash for Transform<N, C, D>
+//     where DefaultAllocator: Allocator<N, DimNameSum<Const<D>, U1>, DimNameSum<Const<D>, U1>>,
+//           Owned<N, DimNameSum<Const<D>, U1>, DimNameSum<Const<D>, U1>>: hash::Hash {
 //     fn hash<H: hash::Hasher>(&self, state: &mut H) {
 //         self.matrix.hash(state);
 //     }
 // }
 
-impl<N: RealField, D: DimNameAdd<U1> + Copy, C: TCategory> Copy for Transform<N, D, C>
+impl<N: RealField, C: TCategory, const D: usize> Copy for Transform<N, C, D>
 where
-    DefaultAllocator: Allocator<N, DimNameSum<D, U1>, DimNameSum<D, U1>>,
-    Owned<N, DimNameSum<D, U1>, DimNameSum<D, U1>>: Copy,
+    Const<D>: DimNameAdd<U1>,
+    DefaultAllocator: Allocator<N, DimNameSum<Const<D>, U1>, DimNameSum<Const<D>, U1>>,
+    Owned<N, DimNameSum<Const<D>, U1>, DimNameSum<Const<D>, U1>>: Copy,
 {
 }
 
-impl<N: RealField, D: DimNameAdd<U1>, C: TCategory> Clone for Transform<N, D, C>
+impl<N: RealField, C: TCategory, const D: usize> Clone for Transform<N, C, D>
 where
-    DefaultAllocator: Allocator<N, DimNameSum<D, U1>, DimNameSum<D, U1>>,
+    Const<D>: DimNameAdd<U1>,
+    DefaultAllocator: Allocator<N, DimNameSum<Const<D>, U1>, DimNameSum<Const<D>, U1>>,
 {
     #[inline]
     fn clone(&self) -> Self {
@@ -192,10 +195,11 @@ where
 }
 
 #[cfg(feature = "serde-serialize")]
-impl<N: RealField, D: DimNameAdd<U1>, C: TCategory> Serialize for Transform<N, D, C>
+impl<N: RealField, C: TCategory, const D: usize> Serialize for Transform<N, C, D>
 where
-    DefaultAllocator: Allocator<N, DimNameSum<D, U1>, DimNameSum<D, U1>>,
-    Owned<N, DimNameSum<D, U1>, DimNameSum<D, U1>>: Serialize,
+    Const<D>: DimNameAdd<U1>,
+    DefaultAllocator: Allocator<N, DimNameSum<Const<D>, U1>, DimNameSum<Const<D>, U1>>,
+    Owned<N, DimNameSum<Const<D>, U1>, DimNameSum<Const<D>, U1>>: Serialize,
 {
     fn serialize<S>(&self, serializer: S) -> Result<S::Ok, S::Error>
     where
@@ -206,29 +210,33 @@ where
 }
 
 #[cfg(feature = "serde-serialize")]
-impl<'a, N: RealField, D: DimNameAdd<U1>, C: TCategory> Deserialize<'a> for Transform<N, D, C>
+impl<'a, N: RealField, C: TCategory, const D: usize> Deserialize<'a> for Transform<N, C, D>
 where
-    DefaultAllocator: Allocator<N, DimNameSum<D, U1>, DimNameSum<D, U1>>,
-    Owned<N, DimNameSum<D, U1>, DimNameSum<D, U1>>: Deserialize<'a>,
+    Const<D>: DimNameAdd<U1>,
+    DefaultAllocator: Allocator<N, DimNameSum<Const<D>, U1>, DimNameSum<Const<D>, U1>>,
+    Owned<N, DimNameSum<Const<D>, U1>, DimNameSum<Const<D>, U1>>: Deserialize<'a>,
 {
     fn deserialize<Des>(deserializer: Des) -> Result<Self, Des::Error>
     where
         Des: Deserializer<'a>,
     {
-        let matrix = MatrixN::<N, DimNameSum<D, U1>>::deserialize(deserializer)?;
+        let matrix = MatrixN::<N, DimNameSum<Const<D>, U1>>::deserialize(deserializer)?;
 
         Ok(Transform::from_matrix_unchecked(matrix))
     }
 }
 
-impl<N: RealField + Eq, D: DimNameAdd<U1>, C: TCategory> Eq for Transform<N, D, C> where
-    DefaultAllocator: Allocator<N, DimNameSum<D, U1>, DimNameSum<D, U1>>
+impl<N: RealField + Eq, C: TCategory, const D: usize> Eq for Transform<N, C, D>
+where
+    Const<D>: DimNameAdd<U1>,
+    DefaultAllocator: Allocator<N, DimNameSum<Const<D>, U1>, DimNameSum<Const<D>, U1>>,
 {
 }
 
-impl<N: RealField, D: DimNameAdd<U1>, C: TCategory> PartialEq for Transform<N, D, C>
+impl<N: RealField, C: TCategory, const D: usize> PartialEq for Transform<N, C, D>
 where
-    DefaultAllocator: Allocator<N, DimNameSum<D, U1>, DimNameSum<D, U1>>,
+    Const<D>: DimNameAdd<U1>,
+    DefaultAllocator: Allocator<N, DimNameSum<Const<D>, U1>, DimNameSum<Const<D>, U1>>,
 {
     #[inline]
     fn eq(&self, right: &Self) -> bool {
@@ -236,14 +244,15 @@ where
     }
 }
 
-impl<N: RealField, D: DimNameAdd<U1>, C: TCategory> Transform<N, D, C>
+impl<N: RealField, C: TCategory, const D: usize> Transform<N, C, D>
 where
-    DefaultAllocator: Allocator<N, DimNameSum<D, U1>, DimNameSum<D, U1>>,
+    Const<D>: DimNameAdd<U1>,
+    DefaultAllocator: Allocator<N, DimNameSum<Const<D>, U1>, DimNameSum<Const<D>, U1>>,
 {
     /// Creates a new transformation from the given homogeneous matrix. The transformation category
     /// of `Self` is not checked to be verified by the given matrix.
     #[inline]
-    pub fn from_matrix_unchecked(matrix: MatrixN<N, DimNameSum<D, U1>>) -> Self {
+    pub fn from_matrix_unchecked(matrix: MatrixN<N, DimNameSum<Const<D>, U1>>) -> Self {
         Transform {
             matrix,
             _phantom: PhantomData,
@@ -263,7 +272,7 @@ where
     /// assert_eq!(t.into_inner(), m);
     /// ```
     #[inline]
-    pub fn into_inner(self) -> MatrixN<N, DimNameSum<D, U1>> {
+    pub fn into_inner(self) -> MatrixN<N, DimNameSum<Const<D>, U1>> {
         self.matrix
     }
 
@@ -271,7 +280,7 @@ where
     /// Deprecated: Use [Transform::into_inner] instead.
     #[deprecated(note = "use `.into_inner()` instead")]
     #[inline]
-    pub fn unwrap(self) -> MatrixN<N, DimNameSum<D, U1>> {
+    pub fn unwrap(self) -> MatrixN<N, DimNameSum<Const<D>, U1>> {
         self.matrix
     }
 
@@ -288,7 +297,7 @@ where
     /// assert_eq!(*t.matrix(), m);
     /// ```
     #[inline]
-    pub fn matrix(&self) -> &MatrixN<N, DimNameSum<D, U1>> {
+    pub fn matrix(&self) -> &MatrixN<N, DimNameSum<Const<D>, U1>> {
         &self.matrix
     }
 
@@ -315,7 +324,7 @@ where
     /// assert_eq!(*t.matrix(), expected);
     /// ```
     #[inline]
-    pub fn matrix_mut_unchecked(&mut self) -> &mut MatrixN<N, DimNameSum<D, U1>> {
+    pub fn matrix_mut_unchecked(&mut self) -> &mut MatrixN<N, DimNameSum<Const<D>, U1>> {
         &mut self.matrix
     }
 
@@ -326,7 +335,7 @@ where
     /// `TAffine` because not all projective transformations are affine (the other way-round is
     /// valid though).
     #[inline]
-    pub fn set_category<CNew: SuperTCategoryOf<C>>(self) -> Transform<N, D, CNew> {
+    pub fn set_category<CNew: SuperTCategoryOf<C>>(self) -> Transform<N, CNew, D> {
         Transform::from_matrix_unchecked(self.matrix)
     }
 
@@ -335,7 +344,7 @@ where
     #[deprecated(
         note = "This method is redundant with automatic `Copy` and the `.clone()` method and will be removed in a future release."
     )]
-    pub fn clone_owned(&self) -> Transform<N, D, C> {
+    pub fn clone_owned(&self) -> Transform<N, C, D> {
         Transform::from_matrix_unchecked(self.matrix.clone_owned())
     }
 
@@ -352,7 +361,7 @@ where
     /// assert_eq!(t.into_inner(), m);
     /// ```
     #[inline]
-    pub fn to_homogeneous(&self) -> MatrixN<N, DimNameSum<D, U1>> {
+    pub fn to_homogeneous(&self) -> MatrixN<N, DimNameSum<Const<D>, U1>> {
         self.matrix().clone_owned()
     }
 
@@ -381,7 +390,7 @@ where
     /// ```
     #[inline]
     #[must_use = "Did you mean to use try_inverse_mut()?"]
-    pub fn try_inverse(self) -> Option<Transform<N, D, C>> {
+    pub fn try_inverse(self) -> Option<Transform<N, C, D>> {
         if let Some(m) = self.matrix.try_inverse() {
             Some(Transform::from_matrix_unchecked(m))
         } else {
@@ -407,7 +416,7 @@ where
     /// ```
     #[inline]
     #[must_use = "Did you mean to use inverse_mut()?"]
-    pub fn inverse(self) -> Transform<N, D, C>
+    pub fn inverse(self) -> Transform<N, C, D>
     where
         C: SubTCategoryOf<TProjective>,
     {
@@ -470,14 +479,14 @@ where
     }
 }
 
-impl<N, D: DimNameAdd<U1>, C> Transform<N, D, C>
+impl<N, C, const D: usize> Transform<N, C, D>
 where
     N: RealField,
     C: TCategory,
-    DefaultAllocator: Allocator<N, DimNameSum<D, U1>, DimNameSum<D, U1>>
-        + Allocator<N, DimNameSum<D, U1>>
-        + Allocator<N, D, D>
-        + Allocator<N, D>,
+    Const<D>: DimNameAdd<U1>,
+    DefaultAllocator: Allocator<N, DimNameSum<Const<D>, U1>, DimNameSum<Const<D>, U1>>
+        + Allocator<N, DimNameSum<Const<D>, U1>>, // + Allocator<N, D, D>
+                                                  // + Allocator<N, D>
 {
     /// Transform the given point by this transformation.
     ///
@@ -492,18 +501,18 @@ where
     ///
     /// This is the same as the multiplication `self * v`.
     #[inline]
-    pub fn transform_vector(&self, v: &VectorN<N, D>) -> VectorN<N, D> {
+    pub fn transform_vector(&self, v: &CVectorN<N, D>) -> CVectorN<N, D> {
         self * v
     }
 }
 
-impl<N: RealField, D: DimNameAdd<U1>, C: TCategory> Transform<N, D, C>
+impl<N: RealField, C: TCategory, const D: usize> Transform<N, C, D>
 where
+    Const<D>: DimNameAdd<U1>,
     C: SubTCategoryOf<TProjective>,
-    DefaultAllocator: Allocator<N, DimNameSum<D, U1>, DimNameSum<D, U1>>
-        + Allocator<N, DimNameSum<D, U1>>
-        + Allocator<N, D, D>
-        + Allocator<N, D>,
+    DefaultAllocator: Allocator<N, DimNameSum<Const<D>, U1>, DimNameSum<Const<D>, U1>>
+        + Allocator<N, DimNameSum<Const<D>, U1>>, // + Allocator<N, D, D>
+                                                  // + Allocator<N, D>
 {
     /// Transform the given point by the inverse of this transformation.
     /// This may be cheaper than inverting the transformation and transforming
@@ -517,27 +526,29 @@ where
     /// This may be cheaper than inverting the transformation and transforming
     /// the vector.
     #[inline]
-    pub fn inverse_transform_vector(&self, v: &VectorN<N, D>) -> VectorN<N, D> {
+    pub fn inverse_transform_vector(&self, v: &CVectorN<N, D>) -> CVectorN<N, D> {
         self.clone().inverse() * v
     }
 }
 
-impl<N: RealField, D: DimNameAdd<U1>> Transform<N, D, TGeneral>
+impl<N: RealField, const D: usize> Transform<N, TGeneral, D>
 where
-    DefaultAllocator: Allocator<N, DimNameSum<D, U1>, DimNameSum<D, U1>>,
+    Const<D>: DimNameAdd<U1>,
+    DefaultAllocator: Allocator<N, DimNameSum<Const<D>, U1>, DimNameSum<Const<D>, U1>>,
 {
     /// A mutable reference to underlying matrix. Use `.matrix_mut_unchecked` instead if this
     /// transformation category is not `TGeneral`.
     #[inline]
-    pub fn matrix_mut(&mut self) -> &mut MatrixN<N, DimNameSum<D, U1>> {
+    pub fn matrix_mut(&mut self) -> &mut MatrixN<N, DimNameSum<Const<D>, U1>> {
         self.matrix_mut_unchecked()
     }
 }
 
-impl<N: RealField, D: DimNameAdd<U1>, C: TCategory> AbsDiffEq for Transform<N, D, C>
+impl<N: RealField, C: TCategory, const D: usize> AbsDiffEq for Transform<N, C, D>
 where
+    Const<D>: DimNameAdd<U1>,
     N::Epsilon: Copy,
-    DefaultAllocator: Allocator<N, DimNameSum<D, U1>, DimNameSum<D, U1>>,
+    DefaultAllocator: Allocator<N, DimNameSum<Const<D>, U1>, DimNameSum<Const<D>, U1>>,
 {
     type Epsilon = N::Epsilon;
 
@@ -552,10 +563,11 @@ where
     }
 }
 
-impl<N: RealField, D: DimNameAdd<U1>, C: TCategory> RelativeEq for Transform<N, D, C>
+impl<N: RealField, C: TCategory, const D: usize> RelativeEq for Transform<N, C, D>
 where
+    Const<D>: DimNameAdd<U1>,
     N::Epsilon: Copy,
-    DefaultAllocator: Allocator<N, DimNameSum<D, U1>, DimNameSum<D, U1>>,
+    DefaultAllocator: Allocator<N, DimNameSum<Const<D>, U1>, DimNameSum<Const<D>, U1>>,
 {
     #[inline]
     fn default_max_relative() -> Self::Epsilon {
@@ -574,10 +586,11 @@ where
     }
 }
 
-impl<N: RealField, D: DimNameAdd<U1>, C: TCategory> UlpsEq for Transform<N, D, C>
+impl<N: RealField, C: TCategory, const D: usize> UlpsEq for Transform<N, C, D>
 where
+    Const<D>: DimNameAdd<U1>,
     N::Epsilon: Copy,
-    DefaultAllocator: Allocator<N, DimNameSum<D, U1>, DimNameSum<D, U1>>,
+    DefaultAllocator: Allocator<N, DimNameSum<Const<D>, U1>, DimNameSum<Const<D>, U1>>,
 {
     #[inline]
     fn default_max_ulps() -> u32 {
diff --git a/src/geometry/transform_alias.rs b/src/geometry/transform_alias.rs
index 58a5ee1e..f869f0e2 100644
--- a/src/geometry/transform_alias.rs
+++ b/src/geometry/transform_alias.rs
@@ -1,17 +1,15 @@
-use crate::base::dimension::{U2, U3};
-
 use crate::geometry::{TAffine, TGeneral, TProjective, Transform};
 
 /// A 2D general transformation that may not be invertible. Stored as a homogeneous 3x3 matrix.
-pub type Transform2<N> = Transform<N, U2, TGeneral>;
+pub type Transform2<N> = Transform<N, TGeneral, 2>;
 /// An invertible 2D general transformation. Stored as a homogeneous 3x3 matrix.
-pub type Projective2<N> = Transform<N, U2, TProjective>;
+pub type Projective2<N> = Transform<N, TProjective, 2>;
 /// A 2D affine transformation. Stored as a homogeneous 3x3 matrix.
-pub type Affine2<N> = Transform<N, U2, TAffine>;
+pub type Affine2<N> = Transform<N, TAffine, 2>;
 
 /// A 3D general transformation that may not be inversible. Stored as a homogeneous 4x4 matrix.
-pub type Transform3<N> = Transform<N, U3, TGeneral>;
+pub type Transform3<N> = Transform<N, TGeneral, 3>;
 /// An invertible 3D general transformation. Stored as a homogeneous 4x4 matrix.
-pub type Projective3<N> = Transform<N, U3, TProjective>;
+pub type Projective3<N> = Transform<N, TProjective, 3>;
 /// A 3D affine transformation. Stored as a homogeneous 4x4 matrix.
-pub type Affine3<N> = Transform<N, U3, TAffine>;
+pub type Affine3<N> = Transform<N, TAffine, 3>;
diff --git a/src/geometry/transform_construction.rs b/src/geometry/transform_construction.rs
index e0826eeb..0d5f8b1e 100644
--- a/src/geometry/transform_construction.rs
+++ b/src/geometry/transform_construction.rs
@@ -4,13 +4,14 @@ use simba::scalar::RealField;
 
 use crate::base::allocator::Allocator;
 use crate::base::dimension::{DimNameAdd, DimNameSum, U1};
-use crate::base::{DefaultAllocator, MatrixN};
+use crate::base::{Const, DefaultAllocator, MatrixN};
 
 use crate::geometry::{TCategory, Transform};
 
-impl<N: RealField, D: DimNameAdd<U1>, C: TCategory> Transform<N, D, C>
+impl<N: RealField, C: TCategory, const D: usize> Transform<N, C, D>
 where
-    DefaultAllocator: Allocator<N, DimNameSum<D, U1>, DimNameSum<D, U1>>,
+    Const<D>: DimNameAdd<U1>,
+    DefaultAllocator: Allocator<N, DimNameSum<Const<D>, U1>, DimNameSum<Const<D>, U1>>,
 {
     /// Creates a new identity transform.
     ///
@@ -42,13 +43,14 @@ where
     /// ```
     #[inline]
     pub fn identity() -> Self {
-        Self::from_matrix_unchecked(MatrixN::<_, DimNameSum<D, U1>>::identity())
+        Self::from_matrix_unchecked(MatrixN::<_, DimNameSum<Const<D>, U1>>::identity())
     }
 }
 
-impl<N: RealField, D: DimNameAdd<U1>, C: TCategory> One for Transform<N, D, C>
+impl<N: RealField, C: TCategory, const D: usize> One for Transform<N, C, D>
 where
-    DefaultAllocator: Allocator<N, DimNameSum<D, U1>, DimNameSum<D, U1>>,
+    Const<D>: DimNameAdd<U1>,
+    DefaultAllocator: Allocator<N, DimNameSum<Const<D>, U1>, DimNameSum<Const<D>, U1>>,
 {
     /// Creates a new identity transform.
     #[inline]
diff --git a/src/geometry/transform_conversion.rs b/src/geometry/transform_conversion.rs
index 6c531f84..0522f7a2 100644
--- a/src/geometry/transform_conversion.rs
+++ b/src/geometry/transform_conversion.rs
@@ -1,74 +1,76 @@
 use simba::scalar::{RealField, SubsetOf};
 
 use crate::base::allocator::Allocator;
-use crate::base::dimension::{DimName, DimNameAdd, DimNameSum, U1};
-use crate::base::{DefaultAllocator, MatrixN};
+use crate::base::dimension::{DimNameAdd, DimNameSum, U1};
+use crate::base::{Const, DefaultAllocator, MatrixN};
 
 use crate::geometry::{SuperTCategoryOf, TCategory, Transform};
 
-impl<N1, N2, D: DimName, C1, C2> SubsetOf<Transform<N2, D, C2>> for Transform<N1, D, C1>
+impl<N1, N2, C1, C2, const D: usize> SubsetOf<Transform<N2, C2, D>> for Transform<N1, C1, D>
 where
     N1: RealField + SubsetOf<N2>,
     N2: RealField,
     C1: TCategory,
     C2: SuperTCategoryOf<C1>,
-    D: DimNameAdd<U1>,
-    DefaultAllocator: Allocator<N1, DimNameSum<D, U1>, DimNameSum<D, U1>>
-        + Allocator<N2, DimNameSum<D, U1>, DimNameSum<D, U1>>,
+    Const<D>: DimNameAdd<U1>,
+    DefaultAllocator: Allocator<N1, DimNameSum<Const<D>, U1>, DimNameSum<Const<D>, U1>>
+        + Allocator<N2, DimNameSum<Const<D>, U1>, DimNameSum<Const<D>, U1>>,
     N1::Epsilon: Copy,
     N2::Epsilon: Copy,
 {
     #[inline]
-    fn to_superset(&self) -> Transform<N2, D, C2> {
+    fn to_superset(&self) -> Transform<N2, C2, D> {
         Transform::from_matrix_unchecked(self.to_homogeneous().to_superset())
     }
 
     #[inline]
-    fn is_in_subset(t: &Transform<N2, D, C2>) -> bool {
+    fn is_in_subset(t: &Transform<N2, C2, D>) -> bool {
         <Self as SubsetOf<_>>::is_in_subset(t.matrix())
     }
 
     #[inline]
-    fn from_superset_unchecked(t: &Transform<N2, D, C2>) -> Self {
+    fn from_superset_unchecked(t: &Transform<N2, C2, D>) -> Self {
         Self::from_superset_unchecked(t.matrix())
     }
 }
 
-impl<N1, N2, D: DimName, C> SubsetOf<MatrixN<N2, DimNameSum<D, U1>>> for Transform<N1, D, C>
+impl<N1, N2, C, const D: usize> SubsetOf<MatrixN<N2, DimNameSum<Const<D>, U1>>>
+    for Transform<N1, C, D>
 where
     N1: RealField + SubsetOf<N2>,
     N2: RealField,
     C: TCategory,
-    D: DimNameAdd<U1>,
-    DefaultAllocator: Allocator<N1, DimNameSum<D, U1>, DimNameSum<D, U1>>
-        + Allocator<N2, DimNameSum<D, U1>, DimNameSum<D, U1>>,
+    Const<D>: DimNameAdd<U1>,
+    DefaultAllocator: Allocator<N1, DimNameSum<Const<D>, U1>, DimNameSum<Const<D>, U1>>
+        + Allocator<N2, DimNameSum<Const<D>, U1>, DimNameSum<Const<D>, U1>>,
     N1::Epsilon: Copy,
     N2::Epsilon: Copy,
 {
     #[inline]
-    fn to_superset(&self) -> MatrixN<N2, DimNameSum<D, U1>> {
+    fn to_superset(&self) -> MatrixN<N2, DimNameSum<Const<D>, U1>> {
         self.matrix().to_superset()
     }
 
     #[inline]
-    fn is_in_subset(m: &MatrixN<N2, DimNameSum<D, U1>>) -> bool {
+    fn is_in_subset(m: &MatrixN<N2, DimNameSum<Const<D>, U1>>) -> bool {
         C::check_homogeneous_invariants(m)
     }
 
     #[inline]
-    fn from_superset_unchecked(m: &MatrixN<N2, DimNameSum<D, U1>>) -> Self {
+    fn from_superset_unchecked(m: &MatrixN<N2, DimNameSum<Const<D>, U1>>) -> Self {
         Self::from_matrix_unchecked(crate::convert_ref_unchecked(m))
     }
 }
 
-impl<N: RealField, D: DimName, C> From<Transform<N, D, C>> for MatrixN<N, DimNameSum<D, U1>>
+impl<N: RealField, C, const D: usize> From<Transform<N, C, D>>
+    for MatrixN<N, DimNameSum<Const<D>, U1>>
 where
-    D: DimNameAdd<U1>,
+    Const<D>: DimNameAdd<U1>,
     C: TCategory,
-    DefaultAllocator: Allocator<N, DimNameSum<D, U1>, DimNameSum<D, U1>>,
+    DefaultAllocator: Allocator<N, DimNameSum<Const<D>, U1>, DimNameSum<Const<D>, U1>>,
 {
     #[inline]
-    fn from(t: Transform<N, D, C>) -> Self {
+    fn from(t: Transform<N, C, D>) -> Self {
         t.to_homogeneous()
     }
 }
diff --git a/src/geometry/transform_ops.rs b/src/geometry/transform_ops.rs
index 01cf4d3d..9a51bbb4 100644
--- a/src/geometry/transform_ops.rs
+++ b/src/geometry/transform_ops.rs
@@ -79,10 +79,10 @@ use crate::geometry::{
  * Indexing.
  *
  */
-impl<N: RealField, D, C: TCategory> Index<(usize, usize)> for Transform<N, D, C>
+impl<N: RealField, C: TCategory, const D: usize> Index<(usize, usize)> for Transform<N, C, D>
 where
-    D: DimName + DimNameAdd<U1>,
-    DefaultAllocator: Allocator<N, DimNameSum<D, U1>, DimNameSum<D, U1>>,
+    Const<D>: DimNameAdd<U1>,
+    DefaultAllocator: Allocator<N, DimNameSum<Const<D>, U1>, DimNameSum<Const<D>, U1>>,
 {
     type Output = N;
 
@@ -93,10 +93,10 @@ where
 }
 
 // Only general transformations are mutably indexable.
-impl<N: RealField, D> IndexMut<(usize, usize)> for Transform<N, D, TGeneral>
+impl<N: RealField, const D: usize> IndexMut<(usize, usize)> for Transform<N, TGeneral, D>
 where
-    D: DimName + DimNameAdd<U1>,
-    DefaultAllocator: Allocator<N, DimNameSum<D, U1>, DimNameSum<D, U1>>,
+    Const<D>: DimNameAdd<U1>,
+    DefaultAllocator: Allocator<N, DimNameSum<Const<D>, U1>, DimNameSum<Const<D>, U1>>,
 {
     #[inline]
     fn index_mut(&mut self, ij: (usize, usize)) -> &mut N {
@@ -108,7 +108,7 @@ where
 md_impl_all!(
     Mul, mul where N: RealField;
     (DimNameSum<D, U1>, DimNameSum<D, U1>), (D, U1) for D: DimNameAdd<U1>, C: TCategory;
-    self: Transform<N, D, C>, rhs: VectorN<N, D>, Output = VectorN<N, D>;
+    self: Transform<N, C, D>, rhs: VectorN<N, D>, Output = VectorN<N, D>;
     [val val] => &self * &rhs;
     [ref val] =>  self * &rhs;
     [val ref] => &self *  rhs;
@@ -133,7 +133,7 @@ md_impl_all!(
     Mul, mul where N: RealField;
     (DimNameSum<D, U1>, DimNameSum<D, U1>), (D, U1) for D: DimNameAdd<U1>, C: TCategory
     where DefaultAllocator: Allocator<N, D, D>;
-    self: Transform<N, D, C>, rhs: Point<N, D>, Output = Point<N, D>;
+    self: Transform<N, C, D>, rhs: Point<N, D>, Output = Point<N, D>;
     [val val] => &self * &rhs;
     [ref val] =>  self * &rhs;
     [val ref] => &self *  rhs;
@@ -170,7 +170,7 @@ md_impl_all!(
 md_impl_all!(
     Mul, mul where N: RealField;
     (DimNameSum<D, U1>, DimNameSum<D, U1>), (D, D) for D: DimNameAdd<U1>, C: TCategoryMul<TAffine>;
-    self: Transform<N, D, C>, rhs: Rotation<N, D>, Output = Transform<N, D, C::Representative>;
+    self: Transform<N, C, D>, rhs: Rotation<N, D>, Output = Transform<N, C::Representative, D>;
     [val val] => Self::Output::from_matrix_unchecked(self.into_inner() * rhs.to_homogeneous());
     [ref val] => Self::Output::from_matrix_unchecked(self.matrix() * rhs.to_homogeneous());
     [val ref] => Self::Output::from_matrix_unchecked(self.into_inner() * rhs.to_homogeneous());
@@ -181,7 +181,7 @@ md_impl_all!(
 md_impl_all!(
     Mul, mul where N: RealField;
     (D, D), (DimNameSum<D, U1>, DimNameSum<D, U1>) for D: DimNameAdd<U1>, C: TCategoryMul<TAffine>;
-    self: Rotation<N, D>, rhs: Transform<N, D, C>, Output = Transform<N, D, C::Representative>;
+    self: Rotation<N, D>, rhs: Transform<N, C, D>, Output = Transform<N, C::Representative, D>;
     [val val] => Self::Output::from_matrix_unchecked(self.to_homogeneous() * rhs.into_inner());
     [ref val] => Self::Output::from_matrix_unchecked(self.to_homogeneous() * rhs.into_inner());
     [val ref] => Self::Output::from_matrix_unchecked(self.to_homogeneous() * rhs.matrix());
@@ -192,7 +192,7 @@ md_impl_all!(
 md_impl_all!(
     Mul, mul where N: RealField;
     (U4, U4), (U4, U1) for C: TCategoryMul<TAffine>;
-    self: Transform<N, U3, C>, rhs: UnitQuaternion<N>, Output = Transform<N, U3, C::Representative>;
+    self: Transform<N, C, 3>, rhs: UnitQuaternion<N>, Output = Transform<N, C::Representative, 3>;
     [val val] => Self::Output::from_matrix_unchecked(self.into_inner() * rhs.to_homogeneous());
     [ref val] => Self::Output::from_matrix_unchecked(self.matrix() * rhs.to_homogeneous());
     [val ref] => Self::Output::from_matrix_unchecked(self.into_inner() * rhs.to_homogeneous());
@@ -203,7 +203,7 @@ md_impl_all!(
 md_impl_all!(
     Mul, mul where N: RealField;
     (U4, U1), (U4, U4) for C: TCategoryMul<TAffine>;
-    self: UnitQuaternion<N>, rhs: Transform<N, U3, C>, Output = Transform<N, U3, C::Representative>;
+    self: UnitQuaternion<N>, rhs: Transform<N, C, 3>, Output = Transform<N, C::Representative, 3>;
     [val val] => Self::Output::from_matrix_unchecked(self.to_homogeneous() * rhs.into_inner());
     [ref val] => Self::Output::from_matrix_unchecked(self.to_homogeneous() * rhs.into_inner());
     [val ref] => Self::Output::from_matrix_unchecked(self.to_homogeneous() * rhs.matrix());
@@ -215,7 +215,7 @@ md_impl_all!(
     Mul, mul where N: RealField;
     (DimNameSum<D, U1>, DimNameSum<D, U1>), (D, U1)
     for D: DimNameAdd<U1>, C: TCategoryMul<TAffine>, R: SubsetOf<MatrixN<N, DimNameSum<D, U1>> >;
-    self: Transform<N, D, C>, rhs: Isometry<N, D, R>, Output = Transform<N, D, C::Representative>;
+    self: Transform<N, C, D>, rhs: Isometry<N, R, D>, Output = Transform<N, C::Representative, D>;
     [val val] => Self::Output::from_matrix_unchecked(self.into_inner() * rhs.to_homogeneous());
     [ref val] => Self::Output::from_matrix_unchecked(self.matrix() * rhs.to_homogeneous());
     [val ref] => Self::Output::from_matrix_unchecked(self.into_inner() * rhs.to_homogeneous());
@@ -227,7 +227,7 @@ md_impl_all!(
     Mul, mul where N: RealField;
     (D, U1), (DimNameSum<D, U1>, DimNameSum<D, U1>)
     for D: DimNameAdd<U1>, C: TCategoryMul<TAffine>, R: SubsetOf<MatrixN<N, DimNameSum<D, U1>> >;
-    self: Isometry<N, D, R>, rhs: Transform<N, D, C>, Output = Transform<N, D, C::Representative>;
+    self: Isometry<N, R, D>, rhs: Transform<N, C, D>, Output = Transform<N, C::Representative, D>;
     [val val] => Self::Output::from_matrix_unchecked(self.to_homogeneous() * rhs.into_inner());
     [ref val] => Self::Output::from_matrix_unchecked(self.to_homogeneous() * rhs.into_inner());
     [val ref] => Self::Output::from_matrix_unchecked(self.to_homogeneous() * rhs.matrix());
@@ -239,7 +239,7 @@ md_impl_all!(
     Mul, mul where N: RealField;
     (DimNameSum<D, U1>, DimNameSum<D, U1>), (D, U1)
     for D: DimNameAdd<U1>, C: TCategoryMul<TAffine>, R: SubsetOf<MatrixN<N, DimNameSum<D, U1>> >;
-    self: Transform<N, D, C>, rhs: Similarity<N, D, R>, Output = Transform<N, D, C::Representative>;
+    self: Transform<N, C, D>, rhs: Similarity<N, R, D>, Output = Transform<N, C::Representative, D>;
     [val val] => Self::Output::from_matrix_unchecked(self.into_inner() * rhs.to_homogeneous());
     [ref val] => Self::Output::from_matrix_unchecked(self.matrix() * rhs.to_homogeneous());
     [val ref] => Self::Output::from_matrix_unchecked(self.into_inner() * rhs.to_homogeneous());
@@ -251,7 +251,7 @@ md_impl_all!(
     Mul, mul where N: RealField;
     (D, U1), (DimNameSum<D, U1>, DimNameSum<D, U1>)
     for D: DimNameAdd<U1>, C: TCategoryMul<TAffine>, R: SubsetOf<MatrixN<N, DimNameSum<D, U1>> >;
-    self: Similarity<N, D, R>, rhs: Transform<N, D, C>, Output = Transform<N, D, C::Representative>;
+    self: Similarity<N, R, D>, rhs: Transform<N, C, D>, Output = Transform<N, C::Representative, D>;
     [val val] => Self::Output::from_matrix_unchecked(self.to_homogeneous() * rhs.into_inner());
     [ref val] => Self::Output::from_matrix_unchecked(self.to_homogeneous() * rhs.into_inner());
     [val ref] => Self::Output::from_matrix_unchecked(self.to_homogeneous() * rhs.matrix());
@@ -270,7 +270,7 @@ md_impl_all!(
 md_impl_all!(
     Mul, mul where N: RealField;
     (DimNameSum<D, U1>, DimNameSum<D, U1>), (D, U1) for D: DimNameAdd<U1>, C: TCategoryMul<TAffine>;
-    self: Transform<N, D, C>, rhs: Translation<N, D>, Output = Transform<N, D, C::Representative>;
+    self: Transform<N, C, D>, rhs: Translation<N, D>, Output = Transform<N, C::Representative, D>;
     [val val] => Self::Output::from_matrix_unchecked(self.into_inner() * rhs.to_homogeneous());
     [ref val] => Self::Output::from_matrix_unchecked(self.matrix() * rhs.to_homogeneous());
     [val ref] => Self::Output::from_matrix_unchecked(self.into_inner() * rhs.to_homogeneous());
@@ -282,7 +282,7 @@ md_impl_all!(
     Mul, mul where N: RealField;
     (D, U1), (DimNameSum<D, U1>, DimNameSum<D, U1>)
     for D: DimNameAdd<U1>, C: TCategoryMul<TAffine>;
-    self: Translation<N, D>, rhs: Transform<N, D, C>, Output = Transform<N, D, C::Representative>;
+    self: Translation<N, D>, rhs: Transform<N, C, D>, Output = Transform<N, C::Representative, D>;
     [val val] => Self::Output::from_matrix_unchecked(self.to_homogeneous() * rhs.into_inner());
     [ref val] => Self::Output::from_matrix_unchecked(self.to_homogeneous() * rhs.into_inner());
     [val ref] => Self::Output::from_matrix_unchecked(self.to_homogeneous() * rhs.matrix());
@@ -304,7 +304,7 @@ md_impl_all!(
 md_impl_all!(
     Div, div where N: RealField;
     (DimNameSum<D, U1>, DimNameSum<D, U1>), (D, D) for D: DimNameAdd<U1>, C: TCategoryMul<TAffine>;
-    self: Transform<N, D, C>, rhs: Rotation<N, D>, Output = Transform<N, D, C::Representative>;
+    self: Transform<N, C, D>, rhs: Rotation<N, D>, Output = Transform<N, C::Representative, D>;
     [val val] => #[allow(clippy::suspicious_arithmetic_impl)] { self * rhs.inverse() };
     [ref val] => #[allow(clippy::suspicious_arithmetic_impl)] { self * rhs.inverse() };
     [val ref] => #[allow(clippy::suspicious_arithmetic_impl)] { self * rhs.inverse() };
@@ -315,7 +315,7 @@ md_impl_all!(
 md_impl_all!(
     Div, div where N: RealField;
     (D, D), (DimNameSum<D, U1>, DimNameSum<D, U1>) for D: DimNameAdd<U1>, C: TCategoryMul<TAffine>;
-    self: Rotation<N, D>, rhs: Transform<N, D, C>, Output = Transform<N, D, C::Representative>;
+    self: Rotation<N, D>, rhs: Transform<N, C, D>, Output = Transform<N, C::Representative, D>;
     [val val] => #[allow(clippy::suspicious_arithmetic_impl)] { self.inverse() * rhs };
     [ref val] => #[allow(clippy::suspicious_arithmetic_impl)] { self.inverse() * rhs };
     [val ref] => #[allow(clippy::suspicious_arithmetic_impl)] { self.inverse() * rhs };
@@ -326,7 +326,7 @@ md_impl_all!(
 md_impl_all!(
     Div, div where N: RealField;
     (U4, U4), (U4, U1) for C: TCategoryMul<TAffine>;
-    self: Transform<N, U3, C>, rhs: UnitQuaternion<N>, Output = Transform<N, U3, C::Representative>;
+    self: Transform<N, C, 3>, rhs: UnitQuaternion<N>, Output = Transform<N, C::Representative, 3>;
     [val val] => #[allow(clippy::suspicious_arithmetic_impl)] { self * rhs.inverse() };
     [ref val] => #[allow(clippy::suspicious_arithmetic_impl)] { self * rhs.inverse() };
     [val ref] => #[allow(clippy::suspicious_arithmetic_impl)] { self * rhs.inverse() };
@@ -337,7 +337,7 @@ md_impl_all!(
 md_impl_all!(
     Div, div where N: RealField;
     (U4, U1), (U4, U4) for C: TCategoryMul<TAffine>;
-    self: UnitQuaternion<N>, rhs: Transform<N, U3, C>, Output = Transform<N, U3, C::Representative>;
+    self: UnitQuaternion<N>, rhs: Transform<N, C, 3>, Output = Transform<N, C::Representative, 3>;
     [val val] => #[allow(clippy::suspicious_arithmetic_impl)] { self.inverse() * rhs };
     [ref val] => #[allow(clippy::suspicious_arithmetic_impl)] { self.inverse() * rhs };
     [val ref] => #[allow(clippy::suspicious_arithmetic_impl)] { self.inverse() * rhs };
@@ -350,7 +350,7 @@ md_impl_all!(
 //          (DimNameSum<D, U1>, DimNameSum<D, U1>), (D, U1)
 //          for D: DimNameAdd<U1>, C: TCategoryMul<TAffine>, R: SubsetOf<MatrixN<N, DimNameSum<D, U1>> >
 //          where SB::Alloc: Allocator<N, DimNameSum<D, U1>, DimNameSum<D, U1> >;
-//          self: Transform<N, D, C>, rhs: Isometry<N, D, R>, Output = Transform<N, D, C::Representative>;
+//          self: Transform<N, C, D>, rhs: Isometry<N, R, D>, Output = Transform<N, C::Representative, D>;
 //          [val val] => Self::Output::from_matrix_unchecked(self.into_inner() * rhs.inverse().to_homogeneous());
 //          [ref val] => Self::Output::from_matrix_unchecked(self.matrix() * rhs.inverse().to_homogeneous());
 //          [val ref] => Self::Output::from_matrix_unchecked(self.into_inner() * rhs.inverse().to_homogeneous());
@@ -363,7 +363,7 @@ md_impl_all!(
 //          (D, U1), (DimNameSum<D, U1>, DimNameSum<D, U1>)
 //          for D: DimNameAdd<U1>, C: TCategoryMul<TAffine>, R: SubsetOf<MatrixN<N, DimNameSum<D, U1>> >
 //          where SA::Alloc: Allocator<N, DimNameSum<D, U1>, DimNameSum<D, U1> >;
-//          self: Isometry<N, D, R>, rhs: Transform<N, D, C>, Output = Transform<N, D, C::Representative>;
+//          self: Isometry<N, R, D>, rhs: Transform<N, C, D>, Output = Transform<N, C::Representative, D>;
 //          [val val] => Self::Output::from_matrix_unchecked(self.to_homogeneous() * rhs.into_inner());
 //          [ref val] => Self::Output::from_matrix_unchecked(self.to_homogeneous() * rhs.into_inner());
 //          [val ref] => Self::Output::from_matrix_unchecked(self.to_homogeneous() * rhs.matrix());
@@ -377,7 +377,7 @@ md_impl_all!(
 //          for D: DimNameAdd<U1>, C: TCategoryMul<TAffine>, R: SubsetOf<MatrixN<N, DimNameSum<D, U1>> >
 //          where SB::Alloc: Allocator<N, D, D >
 //          where SB::Alloc: Allocator<N, DimNameSum<D, U1>, DimNameSum<D, U1> >;
-//          self: Transform<N, D, C>, rhs: Similarity<N, D, R>, Output = Transform<N, D, C::Representative>;
+//          self: Transform<N, C, D>, rhs: Similarity<N, R, D>, Output = Transform<N, C::Representative, D>;
 //          [val val] => Self::Output::from_matrix_unchecked(self.into_inner() * rhs.to_homogeneous());
 //          [ref val] => Self::Output::from_matrix_unchecked(self.matrix() * rhs.to_homogeneous());
 //          [val ref] => Self::Output::from_matrix_unchecked(self.into_inner() * rhs.to_homogeneous());
@@ -391,7 +391,7 @@ md_impl_all!(
 //          for D: DimNameAdd<U1>, C: TCategoryMul<TAffine>, R: SubsetOf<MatrixN<N, DimNameSum<D, U1>> >
 //          where SA::Alloc: Allocator<N, D, D >
 //          where SA::Alloc: Allocator<N, DimNameSum<D, U1>, DimNameSum<D, U1> >;
-//          self: Similarity<N, D, R>, rhs: Transform<N, D, C>, Output = Transform<N, D, C::Representative>;
+//          self: Similarity<N, R, D>, rhs: Transform<N, C, D>, Output = Transform<N, C::Representative, D>;
 //          [val val] => Self::Output::from_matrix_unchecked(self.to_homogeneous() * rhs.into_inner());
 //          [ref val] => Self::Output::from_matrix_unchecked(self.to_homogeneous() * rhs.into_inner());
 //          [val ref] => Self::Output::from_matrix_unchecked(self.to_homogeneous() * rhs.matrix());
@@ -402,7 +402,7 @@ md_impl_all!(
 md_impl_all!(
     Div, div where N: RealField;
     (DimNameSum<D, U1>, DimNameSum<D, U1>), (D, U1) for D: DimNameAdd<U1>, C: TCategoryMul<TAffine>;
-    self: Transform<N, D, C>, rhs: Translation<N, D>, Output = Transform<N, D, C::Representative>;
+    self: Transform<N, C, D>, rhs: Translation<N, D>, Output = Transform<N, C::Representative, D>;
     [val val] => #[allow(clippy::suspicious_arithmetic_impl)] { self * rhs.inverse() };
     [ref val] => #[allow(clippy::suspicious_arithmetic_impl)] { self * rhs.inverse() };
     [val ref] => #[allow(clippy::suspicious_arithmetic_impl)] { self * rhs.inverse() };
@@ -414,7 +414,7 @@ md_impl_all!(
     Div, div where N: RealField;
     (D, U1), (DimNameSum<D, U1>, DimNameSum<D, U1>)
     for D: DimNameAdd<U1>, C: TCategoryMul<TAffine>;
-    self: Translation<N, D>, rhs: Transform<N, D, C>, Output = Transform<N, D, C::Representative>;
+    self: Translation<N, D>, rhs: Transform<N, C, D>, Output = Transform<N, C::Representative, D>;
     [val val] => #[allow(clippy::suspicious_arithmetic_impl)] { self.inverse() * rhs };
     [ref val] => #[allow(clippy::suspicious_arithmetic_impl)] { self.inverse() * rhs };
     [val ref] => #[allow(clippy::suspicious_arithmetic_impl)] { self.inverse() * rhs };
@@ -435,7 +435,7 @@ md_assign_impl_all!(
     MulAssign, mul_assign where N: RealField;
     (DimNameSum<D, U1>, DimNameSum<D, U1>), (D, U1)
     for D: DimNameAdd<U1>, C: TCategory, R: SubsetOf<MatrixN<N, DimNameSum<D, U1>> >;
-    self: Transform<N, D, C>, rhs: Similarity<N, D, R>;
+    self: Transform<N, C, D>, rhs: Similarity<N, R, D>;
     [val] => *self.matrix_mut_unchecked() *= rhs.to_homogeneous();
     [ref] => *self.matrix_mut_unchecked() *= rhs.to_homogeneous();
 );
@@ -445,7 +445,7 @@ md_assign_impl_all!(
     MulAssign, mul_assign where N: RealField;
     (DimNameSum<D, U1>, DimNameSum<D, U1>), (D, U1)
     for D: DimNameAdd<U1>, C: TCategory, R: SubsetOf<MatrixN<N, DimNameSum<D, U1>> >;
-    self: Transform<N, D, C>, rhs: Isometry<N, D, R>;
+    self: Transform<N, C, D>, rhs: Isometry<N, R, D>;
     [val] => *self.matrix_mut_unchecked() *= rhs.to_homogeneous();
     [ref] => *self.matrix_mut_unchecked() *= rhs.to_homogeneous();
 );
@@ -462,7 +462,7 @@ md_assign_impl_all!(
 md_assign_impl_all!(
     MulAssign, mul_assign where N: RealField;
     (DimNameSum<D, U1>, DimNameSum<D, U1>), (D, U1) for D: DimNameAdd<U1>, C: TCategory;
-    self: Transform<N, D, C>, rhs: Translation<N, D>;
+    self: Transform<N, C, D>, rhs: Translation<N, D>;
     [val] => *self.matrix_mut_unchecked() *= rhs.to_homogeneous();
     [ref] => *self.matrix_mut_unchecked() *= rhs.to_homogeneous();
 );
@@ -471,7 +471,7 @@ md_assign_impl_all!(
 md_assign_impl_all!(
     MulAssign, mul_assign where N: RealField;
     (DimNameSum<D, U1>, DimNameSum<D, U1>), (D, D) for D: DimNameAdd<U1>, C: TCategory;
-    self: Transform<N, D, C>, rhs: Rotation<N, D>;
+    self: Transform<N, C, D>, rhs: Rotation<N, D>;
     [val] => *self.matrix_mut_unchecked() *= rhs.to_homogeneous();
     [ref] => *self.matrix_mut_unchecked() *= rhs.to_homogeneous();
 );
@@ -480,7 +480,7 @@ md_assign_impl_all!(
 md_assign_impl_all!(
     MulAssign, mul_assign where N: RealField;
     (U4, U4), (U4, U1) for C: TCategory;
-    self: Transform<N, U3, C>, rhs: UnitQuaternion<N>;
+    self: Transform<N, C, 3>, rhs: UnitQuaternion<N>;
     [val] => *self.matrix_mut_unchecked() *= rhs.to_homogeneous();
     [ref] => *self.matrix_mut_unchecked() *= rhs.to_homogeneous();
 );
@@ -500,7 +500,7 @@ md_assign_impl_all!(
 //          DivAssign, div_assign;
 //          (DimNameSum<D, U1>, DimNameSum<D, U1>), (D, U1)
 //          for D: DimNameAdd<U1>, C: TCategory, R: SubsetOf<MatrixN<N, DimNameSum<D, U1>> >;
-//          self: Transform<N, D, C>, rhs: Similarity<N, D, R>;
+//          self: Transform<N, C, D>, rhs: Similarity<N, R, D>;
 //          [val] => *self *= rhs.inverse();
 //          [ref] => *self *= rhs.inverse();
 //      );
@@ -511,7 +511,7 @@ md_assign_impl_all!(
 //          DivAssign, div_assign;
 //          (DimNameSum<D, U1>, DimNameSum<D, U1>), (D, U1)
 //          for D: DimNameAdd<U1>, C: TCategory, R: SubsetOf<MatrixN<N, DimNameSum<D, U1>> >;
-//          self: Transform<N, D, C>, rhs: Isometry<N, D, R>;
+//          self: Transform<N, C, D>, rhs: Isometry<N, R, D>;
 //          [val] => *self *= rhs.inverse();
 //          [ref] => *self *= rhs.inverse();
 //      );
@@ -520,7 +520,7 @@ md_assign_impl_all!(
 md_assign_impl_all!(
     DivAssign, div_assign where N: RealField;
     (DimNameSum<D, U1>, DimNameSum<D, U1>), (D, U1) for D: DimNameAdd<U1>, C: TCategory;
-    self: Transform<N, D, C>, rhs: Translation<N, D>;
+    self: Transform<N, C, D>, rhs: Translation<N, D>;
     [val] => #[allow(clippy::suspicious_op_assign_impl)] { *self *= rhs.inverse() };
     [ref] => #[allow(clippy::suspicious_op_assign_impl)] { *self *= rhs.inverse() };
 );
@@ -529,7 +529,7 @@ md_assign_impl_all!(
 md_assign_impl_all!(
     DivAssign, div_assign where N: RealField;
     (DimNameSum<D, U1>, DimNameSum<D, U1>), (D, D) for D: DimNameAdd<U1>, C: TCategory;
-    self: Transform<N, D, C>, rhs: Rotation<N, D>;
+    self: Transform<N, C, D>, rhs: Rotation<N, D>;
     [val] => #[allow(clippy::suspicious_op_assign_impl)] { *self *= rhs.inverse() };
     [ref] => #[allow(clippy::suspicious_op_assign_impl)] { *self *= rhs.inverse() };
 );
@@ -538,7 +538,7 @@ md_assign_impl_all!(
 md_assign_impl_all!(
     DivAssign, div_assign where N: RealField;
     (U4, U4), (U4, U1) for C: TCategory;
-    self: Transform<N, U3, C>, rhs: UnitQuaternion<N>;
+    self: Transform<N, C, 3>, rhs: UnitQuaternion<N>;
     [val] => #[allow(clippy::suspicious_op_assign_impl)] { *self *= rhs.inverse() };
     [ref] => #[allow(clippy::suspicious_op_assign_impl)] { *self *= rhs.inverse() };
 );
diff --git a/src/geometry/transform_simba.rs b/src/geometry/transform_simba.rs
index d50843f4..0d116137 100755
--- a/src/geometry/transform_simba.rs
+++ b/src/geometry/transform_simba.rs
@@ -2,19 +2,20 @@ use simba::simd::SimdValue;
 
 use crate::base::allocator::Allocator;
 use crate::base::dimension::{DimNameAdd, DimNameSum, U1};
-use crate::base::{DefaultAllocator, MatrixN, Scalar};
+use crate::base::{Const, DefaultAllocator, MatrixN, Scalar};
 use crate::RealField;
 
 use crate::geometry::{TCategory, Transform};
 
-impl<N: RealField, D: DimNameAdd<U1>, C> SimdValue for Transform<N, D, C>
+impl<N: RealField, C, const D: usize> SimdValue for Transform<N, C, D>
 where
     N::Element: Scalar,
     C: TCategory,
-    DefaultAllocator: Allocator<N, DimNameSum<D, U1>, DimNameSum<D, U1>>
-        + Allocator<N::Element, DimNameSum<D, U1>, DimNameSum<D, U1>>,
+    Const<D>: DimNameAdd<U1>,
+    DefaultAllocator: Allocator<N, DimNameSum<Const<D>, U1>, DimNameSum<Const<D>, U1>>
+        + Allocator<N::Element, DimNameSum<Const<D>, U1>, DimNameSum<Const<D>, U1>>,
 {
-    type Element = Transform<N::Element, D, C>;
+    type Element = Transform<N::Element, C, D>;
     type SimdBool = N::SimdBool;
 
     #[inline]
diff --git a/src/geometry/translation.rs b/src/geometry/translation.rs
index 26bbfd12..1ae452bb 100755
--- a/src/geometry/translation.rs
+++ b/src/geometry/translation.rs
@@ -14,45 +14,44 @@ use abomonation::Abomonation;
 use simba::scalar::{ClosedAdd, ClosedNeg, ClosedSub};
 
 use crate::base::allocator::Allocator;
-use crate::base::dimension::{DimName, DimNameAdd, DimNameSum, U1};
+use crate::base::dimension::{DimNameAdd, DimNameSum, U1};
 use crate::base::storage::Owned;
-use crate::base::{DefaultAllocator, MatrixN, Scalar, VectorN};
+use crate::base::{CVectorN, Const, DefaultAllocator, MatrixN, Scalar};
 
 use crate::geometry::Point;
 
 /// A translation.
 #[repr(C)]
 #[derive(Debug)]
-pub struct Translation<N: Scalar, D: DimName>
-where
-    DefaultAllocator: Allocator<N, D>,
+pub struct Translation<N: Scalar, const D: usize>
+// where
+//     DefaultAllocator: Allocator<N, D>,
 {
     /// The translation coordinates, i.e., how much is added to a point's coordinates when it is
     /// translated.
-    pub vector: VectorN<N, D>,
+    pub vector: CVectorN<N, D>,
 }
 
-impl<N: Scalar + hash::Hash, D: DimName + hash::Hash> hash::Hash for Translation<N, D>
+impl<N: Scalar + hash::Hash, const D: usize> hash::Hash for Translation<N, D>
 where
-    DefaultAllocator: Allocator<N, D>,
-    Owned<N, D>: hash::Hash,
+    // DefaultAllocator: Allocator<N, D>,
+    Owned<N, Const<D>>: hash::Hash,
 {
     fn hash<H: hash::Hasher>(&self, state: &mut H) {
         self.vector.hash(state)
     }
 }
 
-impl<N: Scalar + Copy, D: DimName> Copy for Translation<N, D>
-where
-    DefaultAllocator: Allocator<N, D>,
-    Owned<N, D>: Copy,
+impl<N: Scalar + Copy, const D: usize> Copy for Translation<N, D> where
+    // DefaultAllocator: Allocator<N, D>,
+    Owned<N, Const<D>>: Copy
 {
 }
 
-impl<N: Scalar, D: DimName> Clone for Translation<N, D>
+impl<N: Scalar, const D: usize> Clone for Translation<N, D>
 where
-    DefaultAllocator: Allocator<N, D>,
-    Owned<N, D>: Clone,
+    // DefaultAllocator: Allocator<N, D>,
+    Owned<N, Const<D>>: Clone,
 {
     #[inline]
     fn clone(&self) -> Self {
@@ -65,8 +64,8 @@ impl<N, D> Abomonation for Translation<N, D>
 where
     N: Scalar,
     D: DimName,
-    VectorN<N, D>: Abomonation,
-    DefaultAllocator: Allocator<N, D>,
+    CVectorN<N, D>: Abomonation,
+    // DefaultAllocator: Allocator<N, D>,
 {
     unsafe fn entomb<W: Write>(&self, writer: &mut W) -> IOResult<()> {
         self.vector.entomb(writer)
@@ -82,9 +81,9 @@ where
 }
 
 #[cfg(feature = "serde-serialize")]
-impl<N: Scalar, D: DimName> Serialize for Translation<N, D>
+impl<N: Scalar, const D: usize> Serialize for Translation<N, D>
 where
-    DefaultAllocator: Allocator<N, D>,
+    // DefaultAllocator: Allocator<N, D>,
     Owned<N, D>: Serialize,
 {
     fn serialize<S>(&self, serializer: S) -> Result<S::Ok, S::Error>
@@ -96,29 +95,29 @@ where
 }
 
 #[cfg(feature = "serde-serialize")]
-impl<'a, N: Scalar, D: DimName> Deserialize<'a> for Translation<N, D>
+impl<'a, N: Scalar, const D: usize> Deserialize<'a> for Translation<N, D>
 where
-    DefaultAllocator: Allocator<N, D>,
+    // DefaultAllocator: Allocator<N, D>,
     Owned<N, D>: Deserialize<'a>,
 {
     fn deserialize<Des>(deserializer: Des) -> Result<Self, Des::Error>
     where
         Des: Deserializer<'a>,
     {
-        let matrix = VectorN::<N, D>::deserialize(deserializer)?;
+        let matrix = CVectorN::<N, D>::deserialize(deserializer)?;
 
         Ok(Translation::from(matrix))
     }
 }
 
-impl<N: Scalar, D: DimName> Translation<N, D>
-where
-    DefaultAllocator: Allocator<N, D>,
+impl<N: Scalar, const D: usize> Translation<N, D>
+// where
+//     DefaultAllocator: Allocator<N, D>,
 {
     /// Creates a new translation from the given vector.
     #[inline]
     #[deprecated(note = "Use `::from` instead.")]
-    pub fn from_vector(vector: VectorN<N, D>) -> Translation<N, D> {
+    pub fn from_vector(vector: CVectorN<N, D>) -> Translation<N, D> {
         Translation { vector }
     }
 
@@ -164,15 +163,14 @@ where
     /// assert_eq!(t.to_homogeneous(), expected);
     /// ```
     #[inline]
-    pub fn to_homogeneous(&self) -> MatrixN<N, DimNameSum<D, U1>>
+    pub fn to_homogeneous(&self) -> MatrixN<N, DimNameSum<Const<D>, U1>>
     where
         N: Zero + One,
-        D: DimNameAdd<U1>,
-        DefaultAllocator: Allocator<N, DimNameSum<D, U1>, DimNameSum<D, U1>>,
+        Const<D>: DimNameAdd<U1>,
+        DefaultAllocator: Allocator<N, DimNameSum<Const<D>, U1>, DimNameSum<Const<D>, U1>>,
     {
         let mut res = MatrixN::<N, DimNameSum<D, U1>>::identity();
-        res.fixed_slice_mut::<D, U1>(0, D::dim())
-            .copy_from(&self.vector);
+        res.fixed_slice_mut::<D, U1>(0, D).copy_from(&self.vector);
 
         res
     }
@@ -204,9 +202,9 @@ where
     }
 }
 
-impl<N: Scalar + ClosedAdd, D: DimName> Translation<N, D>
-where
-    DefaultAllocator: Allocator<N, D>,
+impl<N: Scalar + ClosedAdd, const D: usize> Translation<N, D>
+// where
+//     DefaultAllocator: Allocator<N, D>,
 {
     /// Translate the given point.
     ///
@@ -224,9 +222,9 @@ where
     }
 }
 
-impl<N: Scalar + ClosedSub, D: DimName> Translation<N, D>
-where
-    DefaultAllocator: Allocator<N, D>,
+impl<N: Scalar + ClosedSub, const D: usize> Translation<N, D>
+// where
+//     DefaultAllocator: Allocator<N, D>,
 {
     /// Translate the given point by the inverse of this translation.
     ///
@@ -242,11 +240,14 @@ where
     }
 }
 
-impl<N: Scalar + Eq, D: DimName> Eq for Translation<N, D> where DefaultAllocator: Allocator<N, D> {}
+impl<N: Scalar + Eq, const D: usize> Eq for Translation<N, D>
+// where DefaultAllocator: Allocator<N, D>
+{
+}
 
-impl<N: Scalar + PartialEq, D: DimName> PartialEq for Translation<N, D>
-where
-    DefaultAllocator: Allocator<N, D>,
+impl<N: Scalar + PartialEq, const D: usize> PartialEq for Translation<N, D>
+// where
+//     DefaultAllocator: Allocator<N, D>,
 {
     #[inline]
     fn eq(&self, right: &Translation<N, D>) -> bool {
@@ -254,9 +255,9 @@ where
     }
 }
 
-impl<N: Scalar + AbsDiffEq, D: DimName> AbsDiffEq for Translation<N, D>
+impl<N: Scalar + AbsDiffEq, const D: usize> AbsDiffEq for Translation<N, D>
 where
-    DefaultAllocator: Allocator<N, D>,
+    // DefaultAllocator: Allocator<N, D>,
     N::Epsilon: Copy,
 {
     type Epsilon = N::Epsilon;
@@ -272,9 +273,9 @@ where
     }
 }
 
-impl<N: Scalar + RelativeEq, D: DimName> RelativeEq for Translation<N, D>
+impl<N: Scalar + RelativeEq, const D: usize> RelativeEq for Translation<N, D>
 where
-    DefaultAllocator: Allocator<N, D>,
+    // DefaultAllocator: Allocator<N, D>,
     N::Epsilon: Copy,
 {
     #[inline]
@@ -294,9 +295,9 @@ where
     }
 }
 
-impl<N: Scalar + UlpsEq, D: DimName> UlpsEq for Translation<N, D>
+impl<N: Scalar + UlpsEq, const D: usize> UlpsEq for Translation<N, D>
 where
-    DefaultAllocator: Allocator<N, D>,
+    // DefaultAllocator: Allocator<N, D>,
     N::Epsilon: Copy,
 {
     #[inline]
@@ -315,9 +316,9 @@ where
  * Display
  *
  */
-impl<N: Scalar + fmt::Display, D: DimName> fmt::Display for Translation<N, D>
-where
-    DefaultAllocator: Allocator<N, D> + Allocator<usize, D>,
+impl<N: Scalar + fmt::Display, const D: usize> fmt::Display for Translation<N, D>
+// where
+//     DefaultAllocator: Allocator<N, D> + Allocator<usize, D>,
 {
     fn fmt(&self, f: &mut fmt::Formatter) -> fmt::Result {
         let precision = f.precision().unwrap_or(3);
diff --git a/src/geometry/translation_alias.rs b/src/geometry/translation_alias.rs
index 13db0495..554fecc5 100644
--- a/src/geometry/translation_alias.rs
+++ b/src/geometry/translation_alias.rs
@@ -1,21 +1,19 @@
-use crate::base::dimension::{U1, U2, U3, U4, U5, U6};
-
 use crate::geometry::Translation;
 
 /// A 1-dimensional translation.
-pub type Translation1<N> = Translation<N, U1>;
+pub type Translation1<N> = Translation<N, 1>;
 
 /// A 2-dimensional translation.
-pub type Translation2<N> = Translation<N, U2>;
+pub type Translation2<N> = Translation<N, 2>;
 
 /// A 3-dimensional translation.
-pub type Translation3<N> = Translation<N, U3>;
+pub type Translation3<N> = Translation<N, 3>;
 
 /// A 4-dimensional translation.
-pub type Translation4<N> = Translation<N, U4>;
+pub type Translation4<N> = Translation<N, 4>;
 
 /// A 5-dimensional translation.
-pub type Translation5<N> = Translation<N, U5>;
+pub type Translation5<N> = Translation<N, 5>;
 
 /// A 6-dimensional translation.
-pub type Translation6<N> = Translation<N, U6>;
+pub type Translation6<N> = Translation<N, 6>;
diff --git a/src/geometry/translation_construction.rs b/src/geometry/translation_construction.rs
index c1c02862..cfd441d5 100644
--- a/src/geometry/translation_construction.rs
+++ b/src/geometry/translation_construction.rs
@@ -12,15 +12,13 @@ use rand::{
 
 use simba::scalar::{ClosedAdd, SupersetOf};
 
-use crate::base::allocator::Allocator;
-use crate::base::dimension::{DimName, U1, U2, U3, U4, U5, U6};
-use crate::base::{DefaultAllocator, Scalar, VectorN};
+use crate::base::{CVectorN, Scalar};
 
 use crate::geometry::Translation;
 
-impl<N: Scalar, D: DimName> Translation<N, D>
-where
-    DefaultAllocator: Allocator<N, D>,
+impl<N: Scalar, const D: usize> Translation<N, D>
+// where
+//     DefaultAllocator: Allocator<N, D>,
 {
     /// Creates a new identity translation.
     ///
@@ -41,7 +39,7 @@ where
     where
         N: Zero,
     {
-        Self::from(VectorN::<N, D>::from_element(N::zero()))
+        Self::from(CVectorN::<N, D>::from_element(N::zero()))
     }
 
     /// Cast the components of `self` to another type.
@@ -56,15 +54,15 @@ where
     pub fn cast<To: Scalar>(self) -> Translation<To, D>
     where
         Translation<To, D>: SupersetOf<Self>,
-        DefaultAllocator: Allocator<To, D>,
+        // DefaultAllocator: Allocator<To, D>,
     {
         crate::convert(self)
     }
 }
 
-impl<N: Scalar + Zero + ClosedAdd, D: DimName> One for Translation<N, D>
-where
-    DefaultAllocator: Allocator<N, D>,
+impl<N: Scalar + Zero + ClosedAdd, const D: usize> One for Translation<N, D>
+// where
+//     DefaultAllocator: Allocator<N, D>,
 {
     #[inline]
     fn one() -> Self {
@@ -73,27 +71,27 @@ where
 }
 
 #[cfg(feature = "rand-no-std")]
-impl<N: Scalar, D: DimName> Distribution<Translation<N, D>> for Standard
+impl<N: Scalar, const D: usize> Distribution<Translation<N, D>> for Standard
 where
-    DefaultAllocator: Allocator<N, D>,
+    // DefaultAllocator: Allocator<N, D>,
     Standard: Distribution<N>,
 {
     /// Generate an arbitrary random variate for testing purposes.
     #[inline]
     fn sample<'a, G: Rng + ?Sized>(&self, rng: &'a mut G) -> Translation<N, D> {
-        Translation::from(rng.gen::<VectorN<N, D>>())
+        Translation::from(rng.gen::<CVectorN<N, D>>())
     }
 }
 
 #[cfg(feature = "arbitrary")]
-impl<N: Scalar + Arbitrary + Send, D: DimName> Arbitrary for Translation<N, D>
+impl<N: Scalar + Arbitrary + Send, const D: usize> Arbitrary for Translation<N, D>
 where
-    DefaultAllocator: Allocator<N, D>,
+    // DefaultAllocator: Allocator<N, D>,
     Owned<N, D>: Send,
 {
     #[inline]
     fn arbitrary(rng: &mut Gen) -> Self {
-        let v: VectorN<N, D> = Arbitrary::arbitrary(rng);
+        let v: CVectorN<N, D> = Arbitrary::arbitrary(rng);
         Self::from(v)
     }
 }
@@ -104,16 +102,17 @@ where
  *
  */
 macro_rules! componentwise_constructors_impl(
-    ($($doc: expr; $D: ty, $($args: ident:$irow: expr),*);* $(;)*) => {$(
+    ($($doc: expr; $D: expr, $($args: ident:$irow: expr),*);* $(;)*) => {$(
         impl<N: Scalar> Translation<N, $D>
-            where DefaultAllocator: Allocator<N, $D> {
+            // where DefaultAllocator: Allocator<N, $D>
+             {
             #[doc = "Initializes this translation from its components."]
             #[doc = "# Example\n```"]
             #[doc = $doc]
             #[doc = "```"]
             #[inline]
             pub fn new($($args: N),*) -> Self {
-                Self::from(VectorN::<N, $D>::new($($args),*))
+                Self::from(CVectorN::<N, $D>::new($($args),*))
             }
         }
     )*}
@@ -121,15 +120,15 @@ macro_rules! componentwise_constructors_impl(
 
 componentwise_constructors_impl!(
     "# use nalgebra::Translation1;\nlet t = Translation1::new(1.0);\nassert!(t.vector.x == 1.0);";
-    U1, x:0;
+    1, x:0;
     "# use nalgebra::Translation2;\nlet t = Translation2::new(1.0, 2.0);\nassert!(t.vector.x == 1.0 && t.vector.y == 2.0);";
-    U2, x:0, y:1;
+    2, x:0, y:1;
     "# use nalgebra::Translation3;\nlet t = Translation3::new(1.0, 2.0, 3.0);\nassert!(t.vector.x == 1.0 && t.vector.y == 2.0 && t.vector.z == 3.0);";
-    U3, x:0, y:1, z:2;
+    3, x:0, y:1, z:2;
     "# use nalgebra::Translation4;\nlet t = Translation4::new(1.0, 2.0, 3.0, 4.0);\nassert!(t.vector.x == 1.0 && t.vector.y == 2.0 && t.vector.z == 3.0 && t.vector.w == 4.0);";
-    U4, x:0, y:1, z:2, w:3;
+    4, x:0, y:1, z:2, w:3;
     "# use nalgebra::Translation5;\nlet t = Translation5::new(1.0, 2.0, 3.0, 4.0, 5.0);\nassert!(t.vector.x == 1.0 && t.vector.y == 2.0 && t.vector.z == 3.0 && t.vector.w == 4.0 && t.vector.a == 5.0);";
-    U5, x:0, y:1, z:2, w:3, a:4;
+    5, x:0, y:1, z:2, w:3, a:4;
     "# use nalgebra::Translation6;\nlet t = Translation6::new(1.0, 2.0, 3.0, 4.0, 5.0, 6.0);\nassert!(t.vector.x == 1.0 && t.vector.y == 2.0 && t.vector.z == 3.0 && t.vector.w == 4.0 && t.vector.a == 5.0 && t.vector.b == 6.0);";
-    U6, x:0, y:1, z:2, w:3, a:4, b:5;
+    6, x:0, y:1, z:2, w:3, a:4, b:5;
 );
diff --git a/src/geometry/translation_conversion.rs b/src/geometry/translation_conversion.rs
index 9e915073..c49e2735 100644
--- a/src/geometry/translation_conversion.rs
+++ b/src/geometry/translation_conversion.rs
@@ -4,8 +4,8 @@ use simba::scalar::{RealField, SubsetOf, SupersetOf};
 use simba::simd::PrimitiveSimdValue;
 
 use crate::base::allocator::Allocator;
-use crate::base::dimension::{DimName, DimNameAdd, DimNameSum, U1};
-use crate::base::{DefaultAllocator, MatrixN, Scalar, VectorN};
+use crate::base::dimension::{DimNameAdd, DimNameSum, U1};
+use crate::base::{Const, DefaultAllocator, MatrixN, Scalar, VectorN};
 
 use crate::geometry::{
     AbstractRotation, Isometry, Similarity, SuperTCategoryOf, TAffine, Transform, Translation,
@@ -24,11 +24,11 @@ use crate::geometry::{
  * Translation -> Matrix (homogeneous)
  */
 
-impl<N1, N2, D: DimName> SubsetOf<Translation<N2, D>> for Translation<N1, D>
+impl<N1, N2, const D: usize> SubsetOf<Translation<N2, D>> for Translation<N1, D>
 where
     N1: Scalar,
     N2: Scalar + SupersetOf<N1>,
-    DefaultAllocator: Allocator<N1, D> + Allocator<N2, D>,
+    // DefaultAllocator: Allocator<N1, D> + Allocator<N2, D>,
 {
     #[inline]
     fn to_superset(&self) -> Translation<N2, D> {
@@ -48,25 +48,25 @@ where
     }
 }
 
-impl<N1, N2, D: DimName, R> SubsetOf<Isometry<N2, D, R>> for Translation<N1, D>
+impl<N1, N2, R, const D: usize> SubsetOf<Isometry<N2, R, D>> for Translation<N1, D>
 where
     N1: RealField,
     N2: RealField + SupersetOf<N1>,
     R: AbstractRotation<N2, D>,
-    DefaultAllocator: Allocator<N1, D> + Allocator<N2, D>,
+    // DefaultAllocator: Allocator<N1, D> + Allocator<N2, D>,
 {
     #[inline]
-    fn to_superset(&self) -> Isometry<N2, D, R> {
+    fn to_superset(&self) -> Isometry<N2, R, D> {
         Isometry::from_parts(self.to_superset(), R::identity())
     }
 
     #[inline]
-    fn is_in_subset(iso: &Isometry<N2, D, R>) -> bool {
+    fn is_in_subset(iso: &Isometry<N2, R, D>) -> bool {
         iso.rotation == R::identity()
     }
 
     #[inline]
-    fn from_superset_unchecked(iso: &Isometry<N2, D, R>) -> Self {
+    fn from_superset_unchecked(iso: &Isometry<N2, R, D>) -> Self {
         Self::from_superset_unchecked(&iso.translation)
     }
 }
@@ -95,96 +95,96 @@ where
     }
 }
 
-impl<N1, N2, D: DimName, R> SubsetOf<Similarity<N2, D, R>> for Translation<N1, D>
+impl<N1, N2, R, const D: usize> SubsetOf<Similarity<N2, R, D>> for Translation<N1, D>
 where
     N1: RealField,
     N2: RealField + SupersetOf<N1>,
     R: AbstractRotation<N2, D>,
-    DefaultAllocator: Allocator<N1, D> + Allocator<N2, D>,
+    // DefaultAllocator: Allocator<N1, D> + Allocator<N2, D>,
 {
     #[inline]
-    fn to_superset(&self) -> Similarity<N2, D, R> {
+    fn to_superset(&self) -> Similarity<N2, R, D> {
         Similarity::from_parts(self.to_superset(), R::identity(), N2::one())
     }
 
     #[inline]
-    fn is_in_subset(sim: &Similarity<N2, D, R>) -> bool {
+    fn is_in_subset(sim: &Similarity<N2, R, D>) -> bool {
         sim.isometry.rotation == R::identity() && sim.scaling() == N2::one()
     }
 
     #[inline]
-    fn from_superset_unchecked(sim: &Similarity<N2, D, R>) -> Self {
+    fn from_superset_unchecked(sim: &Similarity<N2, R, D>) -> Self {
         Self::from_superset_unchecked(&sim.isometry.translation)
     }
 }
 
-impl<N1, N2, D, C> SubsetOf<Transform<N2, D, C>> for Translation<N1, D>
+impl<N1, N2, C, const D: usize> SubsetOf<Transform<N2, C, D>> for Translation<N1, D>
 where
     N1: RealField,
     N2: RealField + SupersetOf<N1>,
     C: SuperTCategoryOf<TAffine>,
-    D: DimNameAdd<U1>,
-    DefaultAllocator: Allocator<N1, D>
-        + Allocator<N2, D>
-        + Allocator<N1, DimNameSum<D, U1>, DimNameSum<D, U1>>
-        + Allocator<N2, DimNameSum<D, U1>, DimNameSum<D, U1>>,
+    Const<D>: DimNameAdd<U1>,
+    DefaultAllocator: Allocator<N1, DimNameSum<Const<D>, U1>, DimNameSum<Const<D>, U1>>
+        + Allocator<N2, DimNameSum<Const<D>, U1>, DimNameSum<Const<D>, U1>>,
 {
     #[inline]
-    fn to_superset(&self) -> Transform<N2, D, C> {
+    fn to_superset(&self) -> Transform<N2, C, D> {
         Transform::from_matrix_unchecked(self.to_homogeneous().to_superset())
     }
 
     #[inline]
-    fn is_in_subset(t: &Transform<N2, D, C>) -> bool {
+    fn is_in_subset(t: &Transform<N2, C, D>) -> bool {
         <Self as SubsetOf<_>>::is_in_subset(t.matrix())
     }
 
     #[inline]
-    fn from_superset_unchecked(t: &Transform<N2, D, C>) -> Self {
+    fn from_superset_unchecked(t: &Transform<N2, C, D>) -> Self {
         Self::from_superset_unchecked(t.matrix())
     }
 }
 
-impl<N1, N2, D> SubsetOf<MatrixN<N2, DimNameSum<D, U1>>> for Translation<N1, D>
+impl<N1, N2, const D: usize> SubsetOf<MatrixN<N2, DimNameSum<Const<D>, U1>>> for Translation<N1, D>
 where
     N1: RealField,
     N2: RealField + SupersetOf<N1>,
-    D: DimNameAdd<U1>,
-    DefaultAllocator: Allocator<N1, D>
-        + Allocator<N2, D>
-        + Allocator<N1, DimNameSum<D, U1>, DimNameSum<D, U1>>
-        + Allocator<N2, DimNameSum<D, U1>, DimNameSum<D, U1>>,
+    Const<D>: DimNameAdd<U1>,
+    DefaultAllocator: Allocator<N1, DimNameSum<Const<D>, U1>, DimNameSum<Const<D>, U1>>
+        + Allocator<N2, DimNameSum<Const<D>, U1>, DimNameSum<Const<D>, U1>>,
+    // + Allocator<N1, D>
+    // + Allocator<N2, D>
 {
     #[inline]
-    fn to_superset(&self) -> MatrixN<N2, DimNameSum<D, U1>> {
+    fn to_superset(&self) -> MatrixN<N2, DimNameSum<Const<D>, U1>> {
         self.to_homogeneous().to_superset()
     }
 
     #[inline]
-    fn is_in_subset(m: &MatrixN<N2, DimNameSum<D, U1>>) -> bool {
-        let id = m.fixed_slice::<DimNameSum<D, U1>, D>(0, 0);
+    fn is_in_subset(m: &MatrixN<N2, DimNameSum<Const<D>, U1>>) -> bool {
+        let id = m.fixed_slice::<DimNameSum<Const<D>, U1>, D>(0, 0);
 
         // Scalar types agree.
         m.iter().all(|e| SupersetOf::<N1>::is_in_subset(e)) &&
         // The block part does nothing.
         id.is_identity(N2::zero()) &&
         // The normalization factor is one.
-        m[(D::dim(), D::dim())] == N2::one()
+        m[(D, D)] == N2::one()
     }
 
     #[inline]
-    fn from_superset_unchecked(m: &MatrixN<N2, DimNameSum<D, U1>>) -> Self {
-        let t = m.fixed_slice::<D, U1>(0, D::dim());
+    fn from_superset_unchecked(m: &MatrixN<N2, DimNameSum<Const<D>, U1>>) -> Self {
+        let t = m.fixed_slice::<D, U1>(0, D);
         Self {
             vector: crate::convert_unchecked(t.into_owned()),
         }
     }
 }
 
-impl<N: Scalar + Zero + One, D: DimName> From<Translation<N, D>> for MatrixN<N, DimNameSum<D, U1>>
+impl<N: Scalar + Zero + One, const D: usize> From<Translation<N, D>>
+    for MatrixN<N, DimNameSum<Const<D>, U1>>
 where
-    D: DimNameAdd<U1>,
-    DefaultAllocator: Allocator<N, D> + Allocator<N, DimNameSum<D, U1>, DimNameSum<D, U1>>,
+    Const<D>: DimNameAdd<U1>,
+    DefaultAllocator:
+        Allocator<N, DimNameSum<Const<D>, U1>, DimNameSum<Const<D>, U1>> + Allocator<N, Const<D>>,
 {
     #[inline]
     fn from(t: Translation<N, D>) -> Self {
@@ -192,22 +192,22 @@ where
     }
 }
 
-impl<N: Scalar, D: DimName> From<VectorN<N, D>> for Translation<N, D>
-where
-    DefaultAllocator: Allocator<N, D>,
+impl<N: Scalar, const D: usize> From<VectorN<N, Const<D>>> for Translation<N, D>
+// where
+//     DefaultAllocator: Allocator<N, D>,
 {
     #[inline]
-    fn from(vector: VectorN<N, D>) -> Self {
+    fn from(vector: VectorN<N, Const<D>>) -> Self {
         Translation { vector }
     }
 }
 
-impl<N: Scalar + PrimitiveSimdValue, D: DimName> From<[Translation<N::Element, D>; 2]>
+impl<N: Scalar + PrimitiveSimdValue, const D: usize> From<[Translation<N::Element, D>; 2]>
     for Translation<N, D>
 where
     N: From<[<N as simba::simd::SimdValue>::Element; 2]>,
     N::Element: Scalar,
-    DefaultAllocator: Allocator<N, D> + Allocator<N::Element, D>,
+    // DefaultAllocator: Allocator<N, D> + Allocator<N::Element, D>,
 {
     #[inline]
     fn from(arr: [Translation<N::Element, D>; 2]) -> Self {
@@ -218,12 +218,12 @@ where
     }
 }
 
-impl<N: Scalar + PrimitiveSimdValue, D: DimName> From<[Translation<N::Element, D>; 4]>
+impl<N: Scalar + PrimitiveSimdValue, const D: usize> From<[Translation<N::Element, D>; 4]>
     for Translation<N, D>
 where
     N: From<[<N as simba::simd::SimdValue>::Element; 4]>,
     N::Element: Scalar,
-    DefaultAllocator: Allocator<N, D> + Allocator<N::Element, D>,
+    // DefaultAllocator: Allocator<N, D> + Allocator<N::Element, D>,
 {
     #[inline]
     fn from(arr: [Translation<N::Element, D>; 4]) -> Self {
@@ -236,12 +236,12 @@ where
     }
 }
 
-impl<N: Scalar + PrimitiveSimdValue, D: DimName> From<[Translation<N::Element, D>; 8]>
+impl<N: Scalar + PrimitiveSimdValue, const D: usize> From<[Translation<N::Element, D>; 8]>
     for Translation<N, D>
 where
     N: From<[<N as simba::simd::SimdValue>::Element; 8]>,
     N::Element: Scalar,
-    DefaultAllocator: Allocator<N, D> + Allocator<N::Element, D>,
+    // DefaultAllocator: Allocator<N, D> + Allocator<N::Element, D>,
 {
     #[inline]
     fn from(arr: [Translation<N::Element, D>; 8]) -> Self {
@@ -258,12 +258,12 @@ where
     }
 }
 
-impl<N: Scalar + PrimitiveSimdValue, D: DimName> From<[Translation<N::Element, D>; 16]>
+impl<N: Scalar + PrimitiveSimdValue, const D: usize> From<[Translation<N::Element, D>; 16]>
     for Translation<N, D>
 where
     N: From<[<N as simba::simd::SimdValue>::Element; 16]>,
     N::Element: Scalar,
-    DefaultAllocator: Allocator<N, D> + Allocator<N::Element, D>,
+    // DefaultAllocator: Allocator<N, D> + Allocator<N::Element, D>,
 {
     #[inline]
     fn from(arr: [Translation<N::Element, D>; 16]) -> Self {
diff --git a/src/geometry/translation_coordinates.rs b/src/geometry/translation_coordinates.rs
index c422415c..28d9bde2 100644
--- a/src/geometry/translation_coordinates.rs
+++ b/src/geometry/translation_coordinates.rs
@@ -1,10 +1,8 @@
 use std::mem;
 use std::ops::{Deref, DerefMut};
 
-use crate::base::allocator::Allocator;
 use crate::base::coordinates::{X, XY, XYZ, XYZW, XYZWA, XYZWAB};
-use crate::base::dimension::{U1, U2, U3, U4, U5, U6};
-use crate::base::{DefaultAllocator, Scalar};
+use crate::base::Scalar;
 
 use crate::geometry::Translation;
 
@@ -15,9 +13,10 @@ use crate::geometry::Translation;
  */
 
 macro_rules! deref_impl(
-    ($D: ty, $Target: ident $(, $comps: ident)*) => {
+    ($D: expr, $Target: ident $(, $comps: ident)*) => {
         impl<N: Scalar> Deref for Translation<N, $D>
-            where DefaultAllocator: Allocator<N, $D> {
+            // where DefaultAllocator: Allocator<N, $D>
+             {
             type Target = $Target<N>;
 
             #[inline]
@@ -27,7 +26,8 @@ macro_rules! deref_impl(
         }
 
         impl<N: Scalar> DerefMut for Translation<N, $D>
-            where DefaultAllocator: Allocator<N, $D> {
+            // where DefaultAllocator: Allocator<N, $D>
+             {
             #[inline]
             fn deref_mut(&mut self) -> &mut Self::Target {
                 unsafe { mem::transmute(self) }
@@ -36,9 +36,9 @@ macro_rules! deref_impl(
     }
 );
 
-deref_impl!(U1, X, x);
-deref_impl!(U2, XY, x, y);
-deref_impl!(U3, XYZ, x, y, z);
-deref_impl!(U4, XYZW, x, y, z, w);
-deref_impl!(U5, XYZWA, x, y, z, w, a);
-deref_impl!(U6, XYZWAB, x, y, z, w, a, b);
+deref_impl!(1, X, x);
+deref_impl!(2, XY, x, y);
+deref_impl!(3, XYZ, x, y, z);
+deref_impl!(4, XYZW, x, y, z, w);
+deref_impl!(5, XYZWA, x, y, z, w, a);
+deref_impl!(6, XYZWAB, x, y, z, w, a, b);
diff --git a/src/geometry/translation_simba.rs b/src/geometry/translation_simba.rs
index c439a5d2..6d96618f 100755
--- a/src/geometry/translation_simba.rs
+++ b/src/geometry/translation_simba.rs
@@ -1,16 +1,14 @@
 use simba::simd::SimdValue;
 
-use crate::base::allocator::Allocator;
-use crate::base::dimension::DimName;
-use crate::base::{DefaultAllocator, VectorN};
+use crate::base::VectorN;
 use crate::Scalar;
 
 use crate::geometry::Translation;
 
-impl<N: Scalar + SimdValue, D: DimName> SimdValue for Translation<N, D>
+impl<N: Scalar + SimdValue, const D: usize> SimdValue for Translation<N, D>
 where
     N::Element: Scalar,
-    DefaultAllocator: Allocator<N, D> + Allocator<N::Element, D>,
+    // DefaultAllocator: Allocator<N, D> + Allocator<N::Element, D>,
 {
     type Element = Translation<N::Element, D>;
     type SimdBool = N::SimdBool;
diff --git a/src/geometry/unit_complex_conversion.rs b/src/geometry/unit_complex_conversion.rs
index 91736764..f2c02b85 100644
--- a/src/geometry/unit_complex_conversion.rs
+++ b/src/geometry/unit_complex_conversion.rs
@@ -4,7 +4,6 @@ use num_complex::Complex;
 use simba::scalar::{RealField, SubsetOf, SupersetOf};
 use simba::simd::{PrimitiveSimdValue, SimdRealField};
 
-use crate::base::dimension::U2;
 use crate::base::{Matrix2, Matrix3, Scalar};
 use crate::geometry::{
     AbstractRotation, Isometry, Rotation2, Similarity, SuperTCategoryOf, TAffine, Transform,
@@ -17,9 +16,9 @@ use crate::geometry::{
  *
  * UnitComplex -> UnitComplex
  * UnitComplex -> Rotation<U1>
- * UnitComplex -> Isometry<U2>
- * UnitComplex -> Similarity<U2>
- * UnitComplex -> Transform<U2>
+ * UnitComplex -> Isometry<2>
+ * UnitComplex -> Similarity<2>
+ * UnitComplex -> Transform<2>
  * UnitComplex -> Matrix<U3> (homogeneous)
  *
  * NOTE:
@@ -70,68 +69,68 @@ where
     }
 }
 
-impl<N1, N2, R> SubsetOf<Isometry<N2, U2, R>> for UnitComplex<N1>
+impl<N1, N2, R> SubsetOf<Isometry<N2, R, 2>> for UnitComplex<N1>
 where
     N1: RealField,
     N2: RealField + SupersetOf<N1>,
-    R: AbstractRotation<N2, U2> + SupersetOf<Self>,
+    R: AbstractRotation<N2, 2> + SupersetOf<Self>,
 {
     #[inline]
-    fn to_superset(&self) -> Isometry<N2, U2, R> {
+    fn to_superset(&self) -> Isometry<N2, R, 2> {
         Isometry::from_parts(Translation::identity(), crate::convert_ref(self))
     }
 
     #[inline]
-    fn is_in_subset(iso: &Isometry<N2, U2, R>) -> bool {
+    fn is_in_subset(iso: &Isometry<N2, R, 2>) -> bool {
         iso.translation.vector.is_zero()
     }
 
     #[inline]
-    fn from_superset_unchecked(iso: &Isometry<N2, U2, R>) -> Self {
+    fn from_superset_unchecked(iso: &Isometry<N2, R, 2>) -> Self {
         crate::convert_ref_unchecked(&iso.rotation)
     }
 }
 
-impl<N1, N2, R> SubsetOf<Similarity<N2, U2, R>> for UnitComplex<N1>
+impl<N1, N2, R> SubsetOf<Similarity<N2, R, 2>> for UnitComplex<N1>
 where
     N1: RealField,
     N2: RealField + SupersetOf<N1>,
-    R: AbstractRotation<N2, U2> + SupersetOf<Self>,
+    R: AbstractRotation<N2, 2> + SupersetOf<Self>,
 {
     #[inline]
-    fn to_superset(&self) -> Similarity<N2, U2, R> {
+    fn to_superset(&self) -> Similarity<N2, R, 2> {
         Similarity::from_isometry(crate::convert_ref(self), N2::one())
     }
 
     #[inline]
-    fn is_in_subset(sim: &Similarity<N2, U2, R>) -> bool {
+    fn is_in_subset(sim: &Similarity<N2, R, 2>) -> bool {
         sim.isometry.translation.vector.is_zero() && sim.scaling() == N2::one()
     }
 
     #[inline]
-    fn from_superset_unchecked(sim: &Similarity<N2, U2, R>) -> Self {
+    fn from_superset_unchecked(sim: &Similarity<N2, R, 2>) -> Self {
         crate::convert_ref_unchecked(&sim.isometry)
     }
 }
 
-impl<N1, N2, C> SubsetOf<Transform<N2, U2, C>> for UnitComplex<N1>
+impl<N1, N2, C> SubsetOf<Transform<N2, C, 2>> for UnitComplex<N1>
 where
     N1: RealField,
     N2: RealField + SupersetOf<N1>,
     C: SuperTCategoryOf<TAffine>,
 {
     #[inline]
-    fn to_superset(&self) -> Transform<N2, U2, C> {
+    fn to_superset(&self) -> Transform<N2, C, 2> {
         Transform::from_matrix_unchecked(self.to_homogeneous().to_superset())
     }
 
     #[inline]
-    fn is_in_subset(t: &Transform<N2, U2, C>) -> bool {
+    fn is_in_subset(t: &Transform<N2, C, 2>) -> bool {
         <Self as SubsetOf<_>>::is_in_subset(t.matrix())
     }
 
     #[inline]
-    fn from_superset_unchecked(t: &Transform<N2, U2, C>) -> Self {
+    fn from_superset_unchecked(t: &Transform<N2, C, 2>) -> Self {
         Self::from_superset_unchecked(t.matrix())
     }
 }
diff --git a/src/lib.rs b/src/lib.rs
index 8f70b340..a64182be 100644
--- a/src/lib.rs
+++ b/src/lib.rs
@@ -384,9 +384,12 @@ pub fn partial_sort2<'a, T: PartialOrd>(a: &'a T, b: &'a T) -> Option<(&'a T, &'
 /// * [distance](fn.distance.html)
 /// * [distance_squared](fn.distance_squared.html)
 #[inline]
-pub fn center<N: SimdComplexField, D: DimName>(p1: &Point<N, D>, p2: &Point<N, D>) -> Point<N, D>
-where
-    DefaultAllocator: Allocator<N, D>,
+pub fn center<N: SimdComplexField, const D: usize>(
+    p1: &Point<N, D>,
+    p2: &Point<N, D>,
+) -> Point<N, D>
+// where
+//     DefaultAllocator: Allocator<N, D>,
 {
     ((&p1.coords + &p2.coords) * convert::<_, N>(0.5)).into()
 }
@@ -398,12 +401,12 @@ where
 /// * [center](fn.center.html)
 /// * [distance_squared](fn.distance_squared.html)
 #[inline]
-pub fn distance<N: SimdComplexField, D: DimName>(
+pub fn distance<N: SimdComplexField, const D: usize>(
     p1: &Point<N, D>,
     p2: &Point<N, D>,
 ) -> N::SimdRealField
-where
-    DefaultAllocator: Allocator<N, D>,
+// where
+//     DefaultAllocator: Allocator<N, D>,
 {
     (&p2.coords - &p1.coords).norm()
 }
@@ -415,12 +418,12 @@ where
 /// * [center](fn.center.html)
 /// * [distance](fn.distance.html)
 #[inline]
-pub fn distance_squared<N: SimdComplexField, D: DimName>(
+pub fn distance_squared<N: SimdComplexField, const D: usize>(
     p1: &Point<N, D>,
     p2: &Point<N, D>,
 ) -> N::SimdRealField
-where
-    DefaultAllocator: Allocator<N, D>,
+// where
+//     DefaultAllocator: Allocator<N, D>,
 {
     (&p2.coords - &p1.coords).norm_squared()
 }