|Space||Spherical, 4-dimensional space|
|Faces||6 skew squares|
|Abstract & topological properties|
|Symmetry||(A3×2×A1)/2, order 48|
The blended cube or skew cube is a regular skew polyhedron in 4D Euclidean space. It can be constructed by taking a cube and skewing it in the 4th dimension. It is the blend of a cube and the digon. Since the cube is 2-colorable it is abstractly equivalent to the cube. The cube is the only planar regular polyhedron that has this property, although the square tiling and hexagonal tiling are also 2-colorable and thus also have abstractly equivalent blends.
Vertex coordinates[edit | edit source]
For a skew cube with edge length 1 and skew distance its vertex coordinates can be given by
where the total number of negative coordinates is odd.
The vertex coordinates of a skew cube with skew distance and edge length 1 can be given by all permutations of:
These correspond to the vertices of a hexadecachoron with unit edge length.
Gallery[edit | edit source]
Related polytopes[edit | edit source]
The blended cube has the same faces and vertex figure as the blended Petrial tetrahedron, and the two are abstractly equivalent.