Great quasirhombated small stellated hecatonicosachoron

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

Vertex coordinates
The vertices of a great rhombated hecatonicosachoron of edge length 1 are given by all permutations of: plus all even permutations of:
 * $$\left(±\frac12,\,±\frac12,\,±\frac32,\,±\frac{5+2\sqrt5}{2}\right),$$
 * $$\left(±\frac{\sqrt5}{2},\,±\frac{\sqrt5}{2},\,±\frac12,\,±\frac{5+2\sqrt5}{2}\right),$$
 * $$\left(±\frac{1+\sqrt5}{2},\,±\frac{1+\sqrt5}{2},\,±\frac{3+\sqrt5}{2},\,±\frac{5+\sqrt5}{2}\right),$$
 * \left(±\frac{2+\sqrt5}{2},\,±\frac{2+\sqrt5}{2},\,±\frac32,\,±\frac{3+2\sqrt5}{2}\right),
 * $$\left(±\frac{3+\sqrt5}{2},\,±\frac{3+\sqrt5}{2},\,±1,\,±(1+\sqrt5)\right),$$
 * $$\left(±\frac{4+\sqrt5}{2},\,±\frac{4+\sqrrt5}{2},\,±\frac{\sqrt5}{2},\,±\frac{2+\sqrt5}{2}\right),$$
 * $$\left(0,\,±\frac{3-\sqrt5}{4},\,±\frac{2+\sqrt5}{2},\,±\frac{7+5\sqrt5}{4}\right),$$
 * $$\left(0,\,±\frac{3-\sqrt5}{4},\,±\frac{4+\sqrt5}{2},\,±3\frac{3+\sqrt5}{4}\right),$$
 * $$\left(0,\,±\frac12,\,±\frac{7+\sqrt5}{4},\,±\frac{11+3\sqrt5}{4}\right),$$
 * $$\left(0,\,±\frac12,\,±\frac{5+3\sqrt5}{4},\,±5\frac{1+\sqrt5}{4}\right),$$
 * $$\left(0,\,±\frac{\sqrt5-1}{2},\,±\frac{3+\sqrt5}{2},\,±(2+\sqrt5)\right),$$
 * $$\left(±\frac{3-\sqrt5}{4},\,±\frac{\sqrt5-1}{4},\,±\frac{5+2\sqrt5}{2},\,±\frac{1+\sqrt5}{2}\right),$$
 * $$\left(±\frac{3-\sqrt5}{4},\,±1,\,±\frac{3+\sqrt5}{4},\,±\frac{5+2\sqrt5}{2}\right),$$
 * \left(±\frac{3-\sqrt5}{4},\,±\frac{1+\sqrt5}{2},\,±\frac{5+3\sqrt5}{4},\,±\frac{3+2\sqrt5}{2}\right),
 * $$\left(±\frac{3-\sqrt5}{4},\,±\frac{3+\sqrt5}{2},\,±\frac{5+3\sqrt5}{4},\,±\frac{4+\sqrt5}{2}\right),$$
 * $$\left(±\frac{\sqrt5-1}{4},\,±\frac12,\,±\frac{7+3\sqrt5}{4},\,±\frac{5+\sqrt5}{2}\right),$$
 * $$\left(±\frac{\sqrt5-1}{4},\,±\frac{1+\sqrt5}{4},\,±(1+\sqrt5),\,±\frac{3+2\sqrt5}{2}\right),$$
 * $$\left(±\frac{\sqrt5-1}{4},\,±1,\,±\frac{2+\sqrt5}{2},\,±\frac{11+3\sqrt5}{4}\right),$$
 * $$\left(±\frac{\sqrt5-1}{4},\,±\frac{\sqrt5}{2},\,±3\frac{1+\sqrt5}{4},\,±(2+\sqrt5)\right),$$
 * $$\left(±\frac12,\,±1,\,±\frac{5+\sqrt}{4},\,±\frac{7+5\sqrt5}{4}\right),$$
 * $$\left(±\frac12,\,±\frac{\sqrt5}{2},\,±\frac{4+\sqrt5}{2},\,±\frac{3+2\sqrt5}{2}|right),$$
 * $$\left(±\frac12,\,±\frac{3+\sqrt5}{4},\,±\frac{3+\sqrt5}{2},\,±5\frac{1+\sqrt5}{4}\right),$$
 * $$\left(±\frac12,\,±\frac{5+\sqrt5}{4},\,±\frac{5+3\sqrt5}{4},\,±\frac{5+\sqrt5}{2}\right),$$
 * $$\left(±\frac12,\,±3\frac{1+\sqrt5}{4},\,±\frac{5+3\sqrt5}{4},\,±(1+\sqrt5)\right),$$
 * $$\left(±\frac{\sqrt5-1}{2},\,±\frac{1+\sqrt5}{4},\,±\frac{5+2\sqrt5}{2},\,±\frac{3+\sqrt5}{4}\right),$$
 * $$\left(±\frac{\sqrt5-1}{2},\,±\frac{2+\sqrt5}{2},\,±\frac{5+3\sqrt5}{4},\,±\frac{7+3\sqrt5}{4}\right),$$
 * $$\left(±\frac{1+\sqrt5}{4},\,±\frac{\sqrt5}{2},\,±\frac{1+\sqrt5}{2},\,±\frac{7+5\sqrt5}{4}\right),$$
 * $$\left(±\frac{1+\sqrt5}{4},\,±\frac{3+\sqrt5}{4},\,±\frac{4+\sqrt5}{2},\,±\frac{5+\sqrt5}{2}\right),$$
 * $$\left(±\frac{1+\sqrt5}{4},\,±\frac32,\,±\frac{3+\sqrt5}{2},\,±3\frac{3+\sqrt5}{4}\right),$$
 * $$\left(±1,\,±3\frac{1+\sqrt5}{4},\,±\frac{4+\sqrt5}{2},\,±\frac{5+3\sqrt5}{4}\right),$$
 * $$\left(±\frac{\sqrt5}{2},\,±\frac{3+\sqrt5}{4},\,±\frac{1+\sqrt5}{2},\,±\frac{11+3\sqrt5}{4}\right),$$
 * $$\left(±\frac{\sqrt5}{2},\,±\frac{3+\sqrt5}{4},\,±(1+\sqrt5),\,±\frac{7+3\sqrt5}{4}\right),$$
 * $$\left(±\frac{\sqrt5}{2},\,±\frac{1+\sqrt5}{2},\,±3\frac{11+\sqrt5}{4},\,±3\frac{3+\sqrt5}{4}\right),$$
 * $$\left(±\frac{\sqrt5}{2},\,±\frac{7+\sqrt5}{4},\,±\frac{3+\sqrt5}{2},\,±\frac{7+3\sqrt5}{4}\right),$$
 * $$\left(±\frac{3+\sqrt5}{4},\,±\frac32,\,±\frac{5+\sqrt5}{4},\,±(2+\sqrt5)\right),$$
 * $$\left(±\frac{3+\sqrt5}{4},\,±\frac{1+\sqrt5}{2},\,±\frac{2+\sqrt5}{2},\,±5\frac{1+\sqrt5}{4}\right),$$
 * $$\left(±\frac{3+\sqrt5}{4},\,±\frac{5+\sqrt5}{4},\,±(1+\sqrt5),\,±\frac{4+\sqrt5}{2}\right),$$
 * $$\left(±\frac{3+\sqrt5}{4},\,±\frac{2+\sqrt5}{2},\,±3\frac{1+\sqrt5}{4},\,±\frac{5+\sqrt5}{2}\right),$$
 * $$\left(±\frac32,\,±\frac{1+\sqrt5}{2},\,±\frac{7+3\sqrt5}{4},\,±\frac{5+3\sqrt5}{4}\right),$$
 * $$\left(±\frac{1+\sqrt5}{2},\,±\frac{5+\sqrt5}{4},\,±\frac{3+2\sqrt5}{2},\,±\frac{7+\sqrt5}{4}\right).$$