Quasiprismatorhombated hexadecachoron

The quasiprismatorhombated hexadecachoron, or quiproh, is a nonconvex uniform polychoron that consists of 32 triangular prisms, 24 octagrammic prisms, 16 cuboctahedra, and 8 quasitruncated hexahedra. 1 triangular prism, 2 octagrammic prisms, 1 cuboctahedron, and 1 quasitruncated hexahedron join at each vertex. It can be obtained by quasiruncitruncating the tesseract.

The quasiprismatorhombated hexadecachoron can be vertex-inscribed into a sphenoverted trisicositetrachoron. Blending 3 quasiprismatorhombated hexadecachora results in the great rhombic disicositetrachoron.

Vertex coordinates
The vertices of a quasiprismatorhombated hexadecachoron of edge length 1 are given by all permutations of:


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

Related polychora
The quasiprismatorhombated hexadecachoron is the colonel of a 3-member regiment that also includes the great prismatohexadecadisoctachoron and great rhombiprismic tesseractihexadecachoron.