Great rhombated grand hecatonicosachoron

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

Vertex coordinates
The vertices of a great rhombated grand hecatonicosachoron of edge length 1 are given by all permutations of: Plus all even permutations of:
 * $$\left(±\frac12,\,±\frac12,\,±\frac52,\,±\frac{3+2\sqrt5}{2}\right),$$
 * $$\left(±\frac{\sqrt5-1}{2},\,±\frac{\sqrt5-1}{2},\,±\frac{3+\sqrt5}{2},\,±\frac{5+\sqrt5}{2}\right),$$
 * $$\left(±\frac{4+\sqrt5}{2},\,±\frac{4+\sqrt5}{2},\,±\frac{\sqrt5-2}{2},\,±\frac{\sqrt5}{2}\right),$$
 * $$\left(0,\,±\frac12,\,±\frac{11+3\sqrt5}{4},\,±3\frac{\sqrt5-1}{4}\right),$$
 * $$\left(0,\,±\frac12,\,±\frac{9+\sqrt5}{4},\,±\frac{3+5\sqrt5}{4}\right),$$
 * $$\left(0,\,±\frac{3+\sqrt5}{4},\±\frac{4+\sqrt5}{2},\,±\frac{1=5\sqrt5}{4}\right),$$
 * $$\left(0,\,±\frac{1+\sqrt5}{2},\,±\frac{5+\sqrt5}{2},\,±\sqrt5\right),$$
 * $$\left(0,\,±\frac{3+\sqrt5}{4},\,±\frac{6+\sqrt5}{2},\,±\frac{3\sqrt5-1}{4}\right),$$
 * $$\left(±\frac{\sqrt5-2}{2},\,±\frac{\sqrt5-1}{4},\,±\frac{11+3\sqrt5}{4},\,±1\right),$$
 * $$\left(±\frac{\sqrt5-2}{2},\,±\frac{\sqrt5-1}{2},\,±\frac{5+3\sqrt5}{4},\,±\frac{7+3\sqrt5}{4}\right),$$
 * $$\left(±\frac{\sqrt5-2}{2},\,±\frac32,\,±\frac{3+2\sqrt5}{2},\,±\frac{2+\sqrt5}{2}\right),$$
 * \left(±\frac{\sqrt5-1}{4},\,±\frac{\sqrt5-1}{2},\,±\frac{5+\sqrt5}{4},\,±\frac{6+\sqrt5}{2}\right),
 * $$\left(±\frac{\sqrt5-2}{2},\,±\frac{3+\sqrt5}{4},\,±5\frac{1+\sqrt5}{4},\,±\frac{1+\sqrt5}{2}\right),$$
 * $$\left(±\frac{\sqrt5-1}{4},\,±\frac12,\,±2,\,±5\frac{1+\sqrt5}{4}\right),$$
 * $$\left(±\frac{\sqrt5-1}{4},\,±\frac{2+\sqrt5}{2},\,±\frac{3+\sqrt5}{2},\,±\frac{1+5\sqrt5}{4}\right),$$
 * $$\left(±\frac{\sqrt5-1}{4},\,±\sqrt5,\,±3\frac{1+\sqrt5}{4},\,±\frac{4+\sqrt5}{2}\right),$$
 * $$\left(±\frac12,\,±\frac{\sqrt5-1}{2},\,±\frac{5-\sqrt5}{4},\,±\frac{11+3\sqrt5}{4}\right),$$
 * $$\left(±\frac12,\,±\frac{\sqrt5-1}{2},\,±\frac{1+3\sqrt5}{4},\,±5\frac{1+\sqrt5}{4}\right),$$
 * $$\left(±\frac12,\,±\frac{\sqrt5}{2},\,±\frac32,\,±\frac{6+\sqrt5}{2}\right),$$
 * $$\left(±\frac12,\,±\frac{1+\sqrt5}{2},\,±\frac{5+3\sqrt5}{4},\,±\frac{1+5\sqrt5}{4}\right),$$
 * $$\left(±\frac12,\,±\frac{1+3\sqrt5}{4},\,±\frac{7+3\sqrt5}{4},\,±\sqrt5\right),$$
 * $$\left(±\frac12,\,±\frac{2+\sqrt5}{2},\,±\frac52,\,±\frac{4+\sqrt5}{2}\right),$$
 * $$\left(±\frac{\sqrt5-1}{2},\,±\frac{5-\sqrt5}{4},\,±\frac{3+2\sqrt5}{2},\,±3\frac{1+\sqrt5}{4}\right),$$
 * $$\left(±\frac{\sqrt5-1}{2},\,±\frac{3+\sqrt5}{4},\,±\frac32,\,±5\frac{1+\sqrt5}{4}\right),$$
 * $$\left(±\frac{\sqrt5-1}{2},\,±\frac{5+\sqrt5}{4},\,±\frac{3+5\sqrt5}{4},\,±\frac{2+\sqrt5}{2}\right),$$
 * $$\left(±\frac{\sqrt5-1}{2},\,±\frac{3\sqrt5-1}{4},\,±\frac{5+3\sqrt5}{4},\,±\frac{4+\sqrt5}{2}\right),$$
 * $$\left(±\frac{5-\sqrt5}{4},\,±\frac{\sqrt5}{2},\,±\frac{1+\sqrt5}{2},\,±5\frac{1+\sqrt5}{4}\right),$$
 * $$\left(±\frac{5-\sqrt5}{4},\,±\frac{1+\sqrt5}{2},\,±\frac{9+\sqrt5}{4},\,±\frac{4+\sqrt5}{2}\right),$$
 * $$\left(±\frac{5-\sqrt5}{4},\,±2,\,±\frac{7+3\sqrt5}{4},\,±\frac{2+\sqrt5}{2}\right),$$
 * $$\left(±3\frac{\sqrt5-1}{4},\,±\frac{\sqrt5}{2},\,±\frac{3+\sqrt5}{2},\,±\frac{7+3\sqrt5}{4}\right),$$
 * $$\left(±3\frac{\sqrt5-1}{4},\,±\frac{1+\sqrt5}{2},\,±\frac{5+\sqrt5}{4},\,±\frac{3+2\sqrt5}{2}\right),$$
 * $$\left(±1,\,±\frac{\sqrt5}{2},\,±3\frac{1+\sqrt5}{4},\,±\frac{3+5\sqrt5}{4}\right),$$
 * $$\left(±1,\,±\frac{3+\sqrt5}{4},\,±\frac52,\,±\frac{7+3\sqrt5}{4}\right),$$
 * $$\left(±1,\,±\frac{3\sqrt5-1}{4},\,±\frac{1+3\sqrt5}{4},\,±\frac{3+2\sqrt5}{2}\right),$$
 * $$\left(±1,\,±\frac{1+\sqrt5}{2},\,±2,\,±\frac{5+\sqrt5}{2}\right),$$
 * $$\left(±\frac{3+\sqrt5}{4},\,±3\frac{1+\sqrt5}{4},\,±\frac52,\,±\frac{3+\sqrt5}{2}\right),$$
 * $$\left(±\frac32,\,±\frac{1+3\sqrt5}{4},\,±\frac{9+\sqrt5}{4},\,±\frac{3+\sqrt5}{2}\right),$$
 * $$\left(±\frac32,\,±2,\,±\frac{5+3\sqrt5}{4},\,±3\frac{1+\sqrt5}{4}\right),$$
 * $$\left(±\frac{1+\sqrt5}{2},\,±\frac{5+\sqrt5}{4},\,±\frac{5+3\sqrt5}{4},\,±3\frac{1+\sqrt5}{4}\right),$$
 * $$\left(±\frac{5+\sqrt5}{4},\,±\frac{1+3\sqrt5}{4},\,±2,\,±\frac{4+\sqrt5}{2}\right).$$