Great quasidisprismatotesseractihexadecachoron

The great quasidisprismatotesseractihexadecachoron, or gaquidpoth, is a nonconvex uniform polychoron that consists of 32 hexagonal prisms, 24 octagrammic prisms, 16 truncated octahedra, and 8 quasitruncated cuboctahedra. 1 of each type of cell join at each vertex.

The great quasidisprismatotesseractihexadecachoron can be vertex-inscribed into a great prismatotrisicositetrachoron.

Vertex coordinates
Vertex coordinates for a great quasidisprismatotesseractihexadecachoron of edge length 1 are given by all permutations of:
 * $$\left(±\frac{3\sqrt2-1}{2},\,±\frac{2\sqrt2-1}{2},\,±\frac{\sqrt2-1}{2},\,±\frac12\right),$$