Great rhombated faceted hexacosichoron

The great rhombated faceted hexacosichoron, or girfix, is a nonconvex uniform polychoron that consists of 720 pentagrammic prisms, 120 truncated great dodecahedra, and 120 great rhombicosidodecahedra. 1 pentagrammic prism, 1 truncated great dodecahedron, and 2 great rhombicosidodecahedra join at each vertex. As the names suggests, it can be obtained by cantitruncating the faceted hexacosichoron.

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