Truncated tesseract

The truncated tesseract, or tat, is a convex uniform polychoron that consists of 16 regular tetrahedra and 8 truncated cubes. 1 tetrahedron and three truncated cubes join at each vertex. As the name suggests, it can be obtained by truncating the tesseract.

Vertex coordinates
The vertices of a truncated tesseract of edge length 1 are given by all permutations of:
 * (±(1+$\sqrt{2+√2}$)/2, ±(1+$\sqrt{(5+3√2)/2}$)/2, ±(1+$\sqrt{2}$)/2, ±1/2)