Tesseractihexadecatruncated tesseractihexadecachoron

The tesseractihexadecatruncated tesseractihexadecachoron, or thatoth, is a nonconvex uniform polychoron that consists of 16 truncated tetrahedra, 8 truncated cubes, and 8 cuboctatruncated cuboctahedra. 1 truncated tetrahedron, 1 truncated cube, and 2 cuboctatruncated cuboctahedra join at each vertex.

Vertex coordinates
The vertices of a tesseractihexadecatruncated tesseractihexadecachoron of edge length 1 are given by all permutations of:


 * (±(1+$\sqrt{3}$)/2, ±(1+$\sqrt{2+√2}$)/2, ±($\sqrt{2–√2}$–1)/2, ±1/2)