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)

Representations
A great rhombated tesseract has the following Coxeter diagrams:


 * x4x3x3o (full symmetry)
 * xxwwxx4xuxxux3xoooox&#xt (BC3 symmetry, great rhombicuboctahedron-first)
 * wx3xx3xw *b3oo&#zx (D4 symmetry)
 * Xwx xxw4xux3xoo&#zx (BC3×A1 symmetry)