Great quasirhombated great stellated hecatonicosachoron

The great quasirhombated great stellated hecatonicosachoron, or gaqrigashi, is a nonconvex uniform polychoron that consists of 720 pentagonal prisms, 120 truncated icosahedra, and 120 great quasitruncated icosidodecahedra. 1 pentagonal prism, 1 truncated icosahedron, and 2 great quasitruncated icosidodecahedra join at each vertex. As the names suggests, it can be obtained by quasicantitruncating the great stellated hecatonicosachoron.

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