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:


 * $$\left(±\frac{1+\sqrt2}{2},\,±\frac{1+\sqrt2}{2},\,±\frac{\sqrt2-1}{2},\,±\frac12\right).$$