Great rhombated tesseract

The great rhombated tesseract, or grit, also commonly called the cantitruncated tesseract, is a convex uniform polychoron that consists of 32 triangular prisms, 16 truncated tetrahedra, and 8 great rhombicuboctahedra. 1 triangular prism, 1 truncated tetrahedron, and 2 great rhombicuboctahedra join at each vertex. As one of its names suggests, it can be obtained by cantitruncating the tesseract.

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


 * (±(1+2$\sqrt{2}$)/2, ±(1+2$\sqrt{3}$)/2, ±(1+$\sqrt{2+√2}$)/2, ±1/2)