Great quasirhombated great grand stellated hecatonicosachoron

The great quasirhombated great grand stellated hecatonicosachoron, or gaqrigagishi, is a nonconvex uniform polychoron that consists of 1200 triangular prisms, 600 truncated tetrahedra, and 120 great quasitruncated icosidodecahedra. 1 triangular prism, 1 truncated tetrahedron, and 2 great quasitruncated icosidodecahedra join at each vertex. As the name suggests, it can be obtained by quasicantitruncating the great grand stellated hecatonicosachoron.

Vertex coordinates
The vertices of a great quasirhombated great grand stellated hecatonicosachoron of edge length 1 are given by all permutations of: plus all even permutations of:
 * $$\left(±\frac12,\,±\frac12,\,±\frac{2\sqrt5-3}{2},\,±5\frac{\sqrt5-2}{2}\right),$$
 * $$\left(±\frac{3\sqrt5-5}{4},\,±3\frac{3-\sqrt5}{4},\,±\frac{7\sqrt5-13}{4},\,±\frac{7\sqrt5-13}{4}\right),$$
 * $$\left(±\frac{7-3\sqrt5}{4},\,±\frac{7-3\sqrt5}{4},\,±\frac{7\sqrt5-11}{4},\,±\frac{7\sqrt5-15}{4}\right),$$
 * $$\left(0,\,±\frac12,\,±\frac{19-7\sqrt5}{4},\,±\frac{7\sqrt5-13}{4}\right),$$
 * $$\left(0,\,±\frac12,\,±3\frac{7-3\sqrt5}{4},\,±\frac{5\sqrt5-7}{4}\right),$$
 * $$\left(0,\,±\frac{3-\sqrt5}{4},\,±\frac{9-4\sqrt5}{2},\,±\frac{7\sqrt5-11}{4}\right),$$
 * $$\left(0,\,±\frac{3-\sqrt5}{4},\,±\frac{11-4\sqrt5}{2},\,±\frac{5\sqrt5-9}{4}\right),$$
 * $$\left(0,\,±\frac{\sqrt5-1}{2},\,±(5-2\sqrt5),\,±\frac{3\sqrt5-5}{2}\right),$$
 * $$\left(±\frac12,\,±\frac{13-5\sqrt5}{4},\,±\frac{7-3\sqrt5}{2},\,±5\frac{3-\sqrt5}{4}\right),$$
 * $$\left(±\frac12,\,±1,\,±\frac{17-7\sqrt5}{4},\,±\frac{7\sqrt5-15}{4}\right),$$
 * $$\left(±\frac12,\,±\frac{5-\sqrt5}{4},\,±2(\sqrt5-2),\,±\frac{7\sqrt5-13}{4}\right),$$
 * $$\left(±\frac12,\,±\frac{\sqrt5-2}{2},\,±\frac{11-4\sqrt5}{2},\,±\frac{5-2\sqrt5}{2}\right),$$
 * $$\left(±\frac12,\,±\frac{\sqrt5-2}{2},\,±5\frac{\sqrt5-2}{2},\,±\frac{4-\sqrt5}{2}\right),$$
 * $$\left(±\frac12,\,±3\frac{\sqrt5-1}{4},\,±(5-2\sqrt5),\,±\frac{5\sqrt5-11}{4}\right),$$
 * $$\left(±\frac12,\,±\frac{7-3\sqrt5}{4},\,±2(\sqrt5-2),\,±5\frac{3-\sqrt5}{4}\right),$$
 * $$\left(±1,\,±\frac{3-\sqrt5}{4},\,±5\frac{\sqrt5-2}{2},\,±\frac{7-3\sqrt5}{4}\right),$$
 * $$\left(±1,\,±\frac{\sqrt5-2}{2},\,±3\frac{7-3\sqrt5}{4},\,±3\frac{3-\sqrt5}{4}\right),$$
 * $$\left(±1,\,±\frac{3-\sqrt5}{2},\,±2(\sqrt5-2),\,±\frac{7-3\sqrt5}{2}\right),$$
 * $$\left(±1,\,±\frac{3\sqrt5-5}{4},\,±\frac{9-4\sqrt5}{2},\,±\frac{13-5\sqrt5}{4}\right),$$
 * $$\left(±\frac{3-\sqrt5}{4},\,±\frac{5\sqrt5-11}{4},\,±\frac{7\sqrt5-13}{4},\,±5\frac{3-\sqrt5}{4}\right),$$
 * $$\left(±\frac{3-\sqrt5}{4},\,±3\frac{\sqrt5-1}{4},\,±5\frac{\sqrt5-2}{2},\,±\frac{3-\sqrt5}{2}\right),$$
 * $$\left(±\frac{3-\sqrt5}{4},\,±3\frac{3-\sqrt5}{4},\,±\frac{17-7\sqrt5}{4},\,±5\frac{3-\sqrt5}{4}\right),$$
 * $$\left(±\frac{\sqrt5-1}{2},\,±\frac{5-\sqrt5}{4},\,±\frac{3\sqrt5-5}{4},\,±5\frac{\sqrt5-2}{2}\right),$$
 * $$\left(±\frac{\sqrt5-1}{2},\,±\frac{5-2\sqrt5}{2},\,±\frac{7\sqrt5-15}{4},\,±5\frac{3-\sqrt5}{4}\right),$$
 * $$\left(±\frac{5-\sqrt5}{4},\,±3\frac{\sqrt5-1}{4},\,±3\frac{7-3\sqrt5}{4},\,±\frac{7-3\sqrt5}{4}\right),$$
 * $$\left(±\frac{5-\sqrt5}{4},\,±\frac{4-\sqrt5}{2},\,±\frac{17-7\sqrt5}{4},\,±\frac{7-3\sqrt5}{2}\right),$$
 * $$\left(±\frac{5-\sqrt5}{4},\,±\frac{7-3\sqrt5}{4},\,±\frac{19-7\sqrt5}{4},\,±\frac{13-5\sqrt5}{4}\right),$$
 * $$\left(±\frac{\sqrt5-2}{2},\,±\frac{5\sqrt5-11}{4},\,±\frac{7\sqrt5-11}{4},\,±\frac{7-3\sqrt5}{2}\right),$$
 * $$\left(±\frac{\sqrt5-2}{2},\,±\frac{3\sqrt5-5}{2},\,±\frac{7\sqrt5-13}{4},\,±\frac{13-5\sqrt5}{4}\right),$$
 * $$\left(±3\frac{\sqrt5-1}{4},\,±\frac{5\sqrt5-9}{4},\,±\frac{7\sqrt5-15}{4},\,±\frac{13-5\sqrt5}{4}\right),$$
 * $$\left(±3\frac{\sqrt5-1}{4},\,±\frac{5-2\sqrt5}{2},\,±\frac{7\sqrt5-13}{4},\,±\frac{7-3\sqrt5}{2}\right),$$
 * $$\left(±\frac{3-\sqrt5}{2},\,±\frac{3\sqrt5-5}{4},\,±\frac{11-4\sqrt5}{2},\,±\frac{7-3\sqrt5}{4}\right),$$
 * $$\left(±\frac{3-\sqrt5}{2},\,±\frac{4-\sqrt5}{2},\,±\frac{7\sqrt5-15}{4},\,±\frac{7\sqrt5-13}{4}\right),$$
 * $$\left(±\frac{3-\sqrt5}{2},\,±\frac{2\sqrt5-3}{2},\,±\frac{19-7\sqrt5}{4},\,±\frac{5\sqrt5-11}{4}\right),$$
 * $$\left(±\frac{3\sqrt5-5}{4},\,±\frac{5\sqrt5-7}{4},\,±\frac{17-7\sqrt5}{4},\,±\frac{5\sqrt5-11}{4}\right),$$
 * $$\left(±\frac{4-\sqrt5}{2},\,±\frac{7-3\sqrt5}{4},\,±(5-2\sqrt5),\,±3\frac{3-\sqrt5}{4}\right),$$
 * $$\left(±\frac{4-\sqrt5}{2},\,±\frac{2\sqrt5-3}{2},\,±\frac{9-4\sqrt5}{2},\,±\frac{5-2\sqrt5}{2}\right),$$
 * $$\left(±\frac{7-3\sqrt5}{4},\,±\frac{2\sqrt5-3}{2},\,±\frac{17-7\sqrt5}{4},\,±\frac{3\sqrt5-5}{2}\right),$$
 * $$\left(±\frac{7-3\sqrt5}{4},\,±\frac{5\sqrt5-7}{4},\,±2(\sqrt5-2),\,±\frac{5-2\sqrt5}{2}\right),$$
 * $$\left(±\frac{2\sqrt5-3}{2},\,±3\frac{3-\sqrt5}{4},\,±\frac{5\sqrt5-9}{4},\,±2(\sqrt5-2)\right).$$