Great rhombated grand hexacosichoron

The great rhombated grand hexacosichoron, or graggix, is a nonconvex uniform polychoron that consists of 720 pentagrammic prisms, 600 truncated octahedra, and 120 truncated great icosahedra. 1 pentagrammic prism, 1 truncated great icosahedron, and 2 truncated octahedra join at each vertex. As the name suggests, it can be obtained by cantitruncating the grand hexacosichoron.

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