Prismatorhombated tesseract

The prismatorhombated tesseract, or prit, also commonly called the runcitruncated 16-cell, is a convex uniform polychoron that consists of 24 cubes, 32 hexagonal prisms, 16 truncated tetrahedra, and 8 small rhombicuboctahedra. 1 cube, 2 hexagonal prisms, 1 truncated tetrahedron, and 1 small rhombicuboctahedron join at each vertex. As one of its names suggests, it can be obtained by runcitruncating the hexadecachoron.

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


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