Prismatorhombated hexadecachoron

The prismatorhombated hexadecachoron, or proh, also commonly called the runcitruncated tesseract, is a convex uniform polychoron that consists of 32 triangular prisms, 24 octagonal prisms, 16 cuboctahedra, and 8 truncated cubes. 1 triangular prism, 2 octagonal prisms, 1 cuboctahedron, and 1 truncated cubejoin at each vertex. As one of its names suggests, it can be obtained by runcintruncating the tesseract.

The prismatorhombated hexadecachoron can be vertex-inscribed into a small rhombated icositetrachoron.

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


 * (±(1+2$\sqrt{2}$)/2, ±(1+$\sqrt{2}$)/2, ±(1+$\sqrt{2}$)/2, ±1/2)