Tesseractihexadecaquasitruncated prismatotesseractihexadecachoron

The tesseractihexadecaquasitruncated prismatotesseractihexadecachoron, or thaquitpath, is a nonconvex uniform polychoron that consists of 24 octagonal prisms, 16 truncated octahedra, 8 quasitruncated cuboctahedra, and 8 cuboctatruncated cuboctahedra. 1 of each type of cell join at each vertex.

The tesseractihexadecaquasitruncated prismatotesseractihexadecachoron can be vertex-inscribed into a small tetrisicositetrachoron.

Vertex coordinates
Vertex coordinates for a tesseractihexadecaquasitruncated prismatotesseractihexadecachoron of edge length 1 are given by all permutations of:
 * $$\left(±\frac{2\sqrt2-1}{2},\,±\frac{\sqrt2-1}{2},\,±\frac{1+\sqrt2}{2},\,±\frac12\right).$$