Cantellated tesseract

The Cartesian coordinates of the vertices of a cantellated tesseract with edge length 2 is given by all permutations of: The 8 small rhombicuboctahedral cells are joined to each other via their axial square faces.

Their non-axial square faces, which correspond with the edges of a cube, are connected to the triangular prisms.

In geometry, the cantitruncated tesseract or great rhombated tesseract is a uniform 4-polytope (or uniform 4-dimensional polytope) that is bounded by 56 cells: 8 truncated cuboctahedra, 16 truncated tetrahedra, and 32 triangular prisms.

However, the result of this construction would be a polytope which, while its structure would be very similar to that given by cantitruncation, not all of its faces would be uniform.

Alternatively, a uniform cantitruncated tesseract may be constructed by placing 8 uniform truncated cuboctahedra in the hyperplanes of a tesseract's cells, displaced along the coordinate axes such that their octagonal faces coincide.

For an edge length of 2, this construction gives the Cartesian coordinates of its vertices as all permutations of: The 8 truncated cuboctahedra are joined to each other via their octagonal faces, in an arrangement corresponding to the 8 cubical cells of the tesseract.