Truncated tesseract

The Cartesian coordinates of the vertices of a bitruncated tesseract having edge length 2 is given by all permutations of: The truncated octahedra are connected to each other via their square faces, and to the truncated tetrahedra via their hexagonal faces.

The truncated-octahedron-first projection of the bitruncated tesseract into 3D space has a truncated cubical envelope.

Two of the truncated octahedral cells project onto a truncated octahedron inscribed in this envelope, with the square faces touching the centers of the octahedral faces.

This results in the 16 truncated tetrahedral cells, and introduces the 8 octahedra (vertex figures).

The Cartesian coordinates of the vertices of a truncated 16-cell having edge length √2 are given by all permutations, and sign combinations of An alternate construction begins with a demitesseract with vertex coordinates (±3,±3,±3,±3), having an even number of each sign, and truncates it to obtain the permutations of The truncated tetrahedra are joined to each other via their hexagonal faces.

The octahedra are joined to the truncated tetrahedra via their triangular faces.