Tesseractihexadecatruncated prismatotesseractihexadecachoron

The tesseractihexadecatruncated prismatotesseractihexadecachoron, or thatpath, is a nonconvex uniform polychoron that consists of 24 octagrammic prisms, 16 truncated octahedra, 8 great rhombicuboctahedra, and 8 cuboctatruncated cuboctahedra. 1 of each type of cell join at each vertex.

The tesseractihexadecatruncated prismatotesseractihexadecachoron can be vertex-inscribed into a disicositetratruncated disicositetrachoron.

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