Hecatonicosihexacosiquasitruncated hecatonicosihexacosichoron

The hecatonicosihexacosiquasitruncated hecatonicosihexacosichoron, or hixquathix, is a nonconvex uniform polychoron that consists of 600 truncated tetrahedra, 120 quasitruncated great stellated dodecahedra, and 120 icosidodecatruncated icosidodecahedra. 1 truncated tetrahedron, 1 quasitruncated great stellated dodecahedron, and 2 icosidodecatruncated icosidodecahedra join at each vertex.

Vertex coordinates
The vertices of a hecatonicosihexacosiquasitruncated hecatonicosihexacosichoron of edge length 1 are given by all even permutations of:
 * $$\left(0,\,±\frac12,\,±\frac{13-3\sqrt5}{4},\,±\frac{2\sqrt5-3}{2}\right),$$
 * $$\left(0,\,±\frac{3+\sqrt5}{4},\,±\frac{5\sqrt5-11}{4},\,±\frac{2\sqrt5-1}{2}\right),$$
 * $$\left(0,\,±\frac12,\,±3\frac{5-\sqrt5}{4},\,±\frac{3\sqrt5-5}{4}\right),$$
 * $$\left(0,\,±\frac12,\,±\frac{5\sqrt5-9}{4},\,±\frac{5\sqrt5-3}{4}\right),$$
 * $$\left(0,\,±\frac{1+\sqrt5}{2},\,±(3-\sqrt5),\,±(\sqrt5-1)\right),$$
 * $$\left(±\frac{3+\sqrt5}{4},\,±\frac12,\,±\frac{3\sqrt5-1}{4},\,±\frac{3\sqrt5-5}{2}\right),$$
 * $$\left(±\frac{3+\sqrt5}{4},\,±\frac{3-\sqrt5}{4},\,±\frac{3\sqrt5-5}{2},\,±\frac32\right),$$
 * $$\left(±\frac{3+\sqrt5}{4},\,±\frac{\sqrt5-2}{2},\,±\frac{5\sqrt5-7}{4},\,±\frac{5-\sqrt5}{2}\right),$$
 * $$\left(±\frac{3+\sqrt5}{4},\,±\frac{4-\sqrt5}{2},\,±3\frac{3-\sqrt5}{4},\,±\frac{5-\sqrt5}{2}\right),$$
 * $$\left(±\frac12,\,±\frac{5+\sqrt5}{4},\,±\frac{5-\sqrt5}{4},\,±\frac{3\sqrt5-5}{2}\right),$$
 * $$\left(±\frac12,\,±\frac{5+\sqrt5}{4},\,±\frac{11-3\sqrt5}{4},\,±(\sqrt5-2)\right),$$
 * $$\left(±\frac12,\,±1,\,±\frac{5\sqrt5-7}{4},\,±5\frac{\sqrt5-1}{4}\right),$$
 * $$\left(±\frac12,\,±\frac{3-\sqrt5}{4},\,±\frac{1+3\sqrt5}{4},\,±\frac{3\sqrt5-5}{2}\right),$$
 * $$\left(±\frac12,\,±\frac{3-\sqrt5}{4},\,±3\frac{5-\sqrt5}{4},\,±\frac{3-\sqrt5}{2}\right),$$
 * $$\left(±\frac12,\,±\frac{1+3\sqrt5}{4},\,±(3-\sqrt5),\,±\frac{3\sqrt5-5}{4}\right),$$
 * $$\left(±\frac12,\,±\frac{7-\sqrt5}{4},\,±\frac{11-3\sqrt5}{4},\,±\frac{5-\sqrt5}{2}\right),$$
 * $$\left(±\frac12,\,±\frac{3\sqrt5-5}{4},\,±5\frac{\sqrt5-1}{4},\,±\frac{5-\sqrt5}{2}\right),$$
 * $$\left(±\frac{1+\sqrt5}{2},\,±1,\,±\frac{\sqrt5-1}{2},\,±\frac{3\sqrt5-5}{2}\right),$$
 * $$\left(±\frac{1+\sqrt5}{2},\,±\frac{3-\sqrt5}{2},\,±(\sqrt5-2),\,±\frac{5-\sqrt5}{2}\right),$$
 * $$\left(±\frac{5+\sqrt5}{4},\,±\frac{3-\sqrt5}{4},\,±\frac{5\sqrt5-7}{4},\,±3\frac{3-\sqrt5}{4}\right),$$
 * $$\left(±\frac{5+\sqrt5}{4},\,±\frac{3-\sqrt5}{4},\,±\frac{5\sqrt5-11}{4},\,±\frac{7-\sqrt5}{4}\right),$$
 * $$\left(±\frac{5+\sqrt5}{4},\,±\frac{\sqrt5-1}{2},\,±\frac{5\sqrt5-9}{4},\,±\frac{4-\sqrt5}{2}\right),$$
 * $$\left(±1,\,±\frac{1+3\sqrt5}{4},\,±\frac{5\sqrt5-11}{4},\,±\frac{\sqrt5-2}{2}\right),$$
 * $$\left(±1,\,±\frac32,\,±\frac{11-3\sqrt5}{4},\,±3\frac{3-\sqrt5}{4}\right),$$
 * $$\left(±1,\,±\frac{5-\sqrt5}{4},\,±\frac{13-3\sqrt5}{4},\,±\frac{4-\sqrt5}{2}\right),$$
 * $$\left(±\frac{3-\sqrt5}{4},\,±\frac32,\,±(\sqrt5-2),\,±5\frac{\sqrt5-1}{4}\right),$$
 * $$\left(±\frac{3-\sqrt5}{4},\,±\frac{\sqrt5-1}{2},\,±3\frac{5-\sqrt5}{4},\,±\frac{\sqrt5-2}{2}\right),$$
 * $$\left(±\frac{3-\sqrt5}{4},\,±\frac{3\sqrt5-1}{4},\,±\frac{13-3\sqrt5}{4},\,±\frac{3\sqrt5-5}{4}\right),$$
 * $$\left(±\frac{1+3\sqrt5}{4},\,±\frac{3\sqrt5-5}{4},\,±(\sqrt5-2),\,±\frac{4-\sqrt5}{2}\right),$$
 * $$\left(±\frac{3-\sqrt5}{4},\,±\frac{3\sqrt5-5}{4},\,±\frac{5\sqrt5-3}{4},\,±3\frac{3-\sqrt5}{4}\right),$$
 * $$\left(±\frac{3-\sqrt5}{4},\,±\frac{4-\sqrt5}{2},\,±(\sqrt5-1),\,±5\frac{\sqrt5-1}{4}\right),$$
 * $$\left(±\frac{1+3\sqrt5}{4},\,±\frac{3-\sqrt5}{2},\,±\frac{2\sqrt5-3}{2},\,±3\frac{3-\sqrt5}{4}\right),$$
 * $$\left(±\frac32,\,±\frac{5-\sqrt5}{4},\,±(3-\sqrt5),\,±\frac{7-\sqrt5}{4}\right),$$
 * $$\left(±\frac32,\,±\frac{3\sqrt5-1}{4},\,±\frac{5\sqrt5-9}{4},\,±\frac{3-\sqrt5}{2}\right),$$
 * $$\left(±\frac{\sqrt5-1}{2},\,±\frac{7-\sqrt5}{4},\,±\frac{2\sqrt5-3}{2},\,±5\frac{\sqrt5-1}{4}\right),$$
 * $$\left(±\frac{\sqrt5-1}{2},\,±\frac{2\sqrt5-1}{2},\,±\frac{11-3\sqrt5}{4},\,±\frac{3\sqrt5-5}{4}\right),$$
 * $$\left(±\frac{5-\sqrt5}{4},\,±\frac{\sqrt5-2}{2},\,±\frac{5\sqrt5-3}{4},\,±(\sqrt5-2)\right),$$
 * $$\left(±\frac{5-\sqrt5}{4},\,±\frac{3-\sqrt5}{2},\,±\frac{2\sqrt5-1}{2},\,±\frac{5\sqrt5-7}{4}\right),$$
 * $$\left(±\frac{3\sqrt5-1}{4},\,±\frac{\sqrt5-2}{2},\,±(\sqrt5-1),\,±\frac{11-3\sqrt5}{4}\right),$$
 * $$\left(±\frac{3\sqrt5-1}{4},\,±\frac{7-\sqrt5}{4},\,±\frac{3\sqrt5-5}{4},\,±\frac{5\sqrt5-7}{4}\right).$$