Great rhombated hexacosichoron

The great rhombated hexacosichoron, or grix, also commonly called the cantitruncated 600-cell, is a convex uniform polychoron that consists of 720 pentagonal prisms, 600 truncated octahedra, and 120 truncated icosahedra. 1 pentagonal prism, 1 truncated icosahedron, and 2 truncated octahedra join at each vertex. As one of its names suggests, it can be obtained by cantitruncating the hexacoscichoron.

Vertex coordinates
The vertices of a great rhombated hexacosichoron of edge length 1 are given by all permutations of: plus all even permutations of:
 * $$\left(±\frac12,\,±\frac12,\,±\frac{4+3\sqrt5}{2},\,±\frac{8+3\sqrt5}{2}\right),$$
 * $$\left(±\frac12,\,±\frac32,\,±3\frac{2+\sqrt5}{2},\,±3\frac{2+\sqrt5}{2}\right),$$
 * $$\left(±1,\,±1,\,±\frac{5+3\sqrt5}{2},\,±\frac{7+3\sqrt5}{2}\right),$$
 * $$\left(0,\,±\frac12,\,±3\frac{1+\sqrt5}{4},\,±3\frac{5+3\sqrt5}{4}\right),$$
 * $$\left(0,\,±\frac12,\,±5\frac{1+\sqrt5}{4},\,±\frac{17+7\sqrt5}{4}\right),$$
 * $$\left(0,\,±1,\,±(1+\sqrt5),\,±2(2+\sqrt5)\right),$$
 * $$\left(0,\,±\frac{11+3\sqrt5}{4},\,±\frac{11+5\sqrt5}{4},\,±\frac{7+2\sqrt5}{2}\right),$$
 * $$\left(0,\,±\frac{5+2\sqrt5}{2},\,±\frac{13+5\sqrt5}{4},\,±\frac{13+3\sqrt5}{4}\right),$$
 * $$\left(±\frac12,\,±\frac{1+\sqrt5}{4},\,±3\frac{3+\sqrt5}{2},\,±\frac{7+5\sqrt5}{4}\right),$$
 * $$\left(±\frac12,\,±\frac{1+\sqrt5}{2},\,±3\frac{5+3\sqrt5}{4},\,±\frac{5+\sqrt5}{4}\right),$$
 * $$\left(±\frac12,\,±\frac{7+\sqrt5}{4},\,±3\frac{1+\sqrt5}{4},\,±2(2+\sqrt5)\right),$$
 * $$\left(±\frac12,\,±3\frac{1+\sqrt5}{4},\,±3\frac{3+\sqrt5}{2},\,±3\frac{3+\sqrt5}{4}\right),$$
 * $$\left(±\frac12,\,±\frac{4+\sqrt5}{2},\,±3\frac{2+\sqrt5}{2},\,±\frac{7+2\sqrt5}{2}\right),$$
 * $$\left(±\frac12,\,±\frac{7+3\sqrt5}{4},\,±\frac{7+3\sqrt5}{2},\,±\frac{13+3\sqrt5}{4}\right),$$
 * $$\left(±\frac{1+\sqrt5}{4},\,±1,\,±\frac{2+\sqrt5}{2},\,±3\frac{5+3\sqrt5}{4}\right),$$
 * $$\left(±\frac{1+\sqrt5}{4},\,±\frac32,\,±\frac{5+3\sqrt5}{4},\,±2(2+\sqrt5)\right),$$
 * $$\left(±\frac{1+\sqrt5}{4},\,±3\frac{3+\sqrt5}{4},\,±\frac{5+3\sqrt5}{2},\,±\frac{7+2\sqrt5}{2}\right),$$
 * $$\left(±\frac{1+\sqrt5}{4},\,±(2+\sqrt5),\,±3\frac{2+\sqrt5}{2},\,±\frac{13+3\sqrt5}{4}\right),$$
 * $$\left(±1,\,±\frac{1+\sqrt5}{2},\,±3\frac{3+\sqrt5}{2},\,±(2+\sqrt5)\right),$$
 * $$\left(±1,\,±\frac{7+\sqrt5}{4},\,±3\frac{2+\sqrt5}{2},\,±\frac{13+5\sqrt5}{4}\right),$$
 * $$\left(±1,\,±3\frac{1+\sqrt5}{4},\,±\frac{17+7\sqrt5}{4},\,±\frac{4+\sqrt5}{2}\right),$$
 * $$\left(±1,\,±\frac{5+3\sqrt5}{4},\,±\frac{8+3\sqrt5}{2},\,±\frac{11+3\sqrt5}{4}\right),$$
 * $$\left(±\frac32,\,±\frac{1+\sqrt5}{2},\,±\frac{17+7\sqrt5}{4},\,±\frac{7+3\sqrt5}{4}\right),$$
 * $$\left(±\frac32,\,±\frac{5+\sqrt5}{4},\,±\frac{7+3\sqrt5}{2},\,±\frac{11+5\sqrt5}{4}\right),$$
 * $$\left(±\frac32,\,±\frac{2+\sqrt5}{2},\,±\frac{8+3\sqrt5}{2},\,±\frac{5+2\sqrt5}{2}\right),$$
 * $$\left(±\frac{1+\sqrt5}{2},\,±3\frac{3+\sqrt5}{4},\,±\frac{4+3\sqrt5}{2},\,±\frac{13+5\sqrt5}{4}\right),$$
 * $$\left(±\frac{1+\sqrt5}{2},\,±\frac{11+3\sqrt5}{4},\,±\frac{7+5\sqrt5}{4},\,±3\frac{2+\sqrt5}{2}\right),$$
 * $$\left(±\frac{5+\sqrt5}{4},\,±\frac{7+\sqrt5}{4},\,±\frac{5+3\sqrt5}{2},\,±3\frac{2+\sqrt5}{2}\right),$$
 * $$\left(±\frac{5+\sqrt5}{4},\,±\frac{5+3\sqrt5}{4},\,±3\frac{3+\sqrt5}{2},\,±\frac{4+\sqrt5}{2}\right),$$
 * $$\left(±\frac{5+\sqrt5}{4},\,±(1+\sqrt5),\,±\frac{8+3\sqrt5}{2},\,±3\frac{3+\sqrt5}{4}\right),$$
 * $$\left(±\frac{2+\sqrt5}{2},\,±\frac{7+\sqrt5}{4},\,±\frac{7+3\sqrt5}{4},\,±3\frac{3+\sqrt5}{2}\right),$$
 * $$\left(±\frac{2+\sqrt5}{2},\,±\frac{4+\sqrt5}{2},\,±\frac{4+3\sqrt5}{2},\,±3\frac{2+\sqrt5}{2}\right),$$
 * $$\left(±\frac{2+\sqrt5}{2},\,±3\frac{3+\sqrt5}{4},\,±5\frac{1+\sqrt5}{4},\,±\frac{7+3\sqrt5}{2}\right),$$
 * $$\left(±\frac{7+\sqrt5}{4},\,±3\frac{1+\sqrt5}{4},\,±\frac{8+3\sqrt5}{2},\,±(2+\sqrt5)\right),$$
 * $$\left(±3\frac{1+\sqrt5}{4},\,±\frac{4+\sqrt5}{2},\,±\frac{7+5\sqrt5}{4},\,±\frac{7+3\sqrt5}{2}\right),$$
 * $$\left(±3\frac{1+\sqrt5}{4},\,±(2+\sqrt5),\,±\frac{4+3\sqrt5}{2},\,±\frac{11+5\sqrt5}{4}\right),$$
 * $$\left(±3\frac{1+\sqrt5}{4},\,±\frac{7+5\sqrt5}{4},\,±\frac{5+3\sqrt5}{2},\,±\frac{5+2\sqrt5}{2}\right),$$
 * $$\left(±\frac{5+3\sqrt5}{4},\,±\frac{7+3\sqrt5}{4},\,±\frac{4+3\sqrt5}{2},\,±\frac{5+3\sqrt5}{2}\right),$$
 * $$\left(±\frac{5+3\sqrt5}{4},\,±5\frac{1+\sqrt5}{4},\,±3\frac{2+\sqrt5}{2},\,±(2+\sqrt5)\right),$$
 * $$\left(±(1+\sqrt5),\,±\frac{7+3\sqrt5}{4},\,±\frac{7+5\sqrt5}{4},\,±3\frac{2+\sqrt5}{2}\right).$$