Great quasirhombated great grand hecatonicosachoron

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

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