Great quasirhombated great faceted hexacosichoron

The great quasirhombated great faceted hexacosichoron, or gaqrigafix, is a nonconvex uniform polychoron that consists of 720 pentagonal prisms, 120 quasitruncated small stellated dodecahedra, and 120 great quasitruncated icosidodecahedra. 1 pentagonal prism, 1 quasitruncated small stellated dodecahedron, and 2 great quasitruncated icosidodecahedra join at each vertex. As the names suggests, it can be obtained by quasicantitruncating the great faceted hexacosichoron.

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