Hecatonicosihexacosiquasitruncated prismatohecatonicosihexacosichoron

The hecatonicosihexacosiquasitruncated prismatohecatonicosihexacosichoron, or hixquitphix, is a nonconvex uniform polychoron that consists of 720 decagonal prisms, 600 truncated octahedra, 120 great quasitruncated icosidodecahedra, and 120 icosidodecatruncated icosidodecahedra. 1 of each type of cell join at each vertex.

Vertex coordinates
Vertex coordinates for a hecatonicosihexacosiquasitruncated prismatohecatonicosihexacosichoron of edge length 1 are given by all permutations of: plus all even permutations of:
 * $$\left(±\frac12,\,±\frac12,\,±\frac{2\sqrt5-3}{2},\,±\frac{9-2\sqrt5}{2}\right),$$
 * $$\left(±\frac12,\,±\frac12,\,±\frac{3\sqrt5-2}{2},\,±3\frac{\sqrt5-2}{2}\right),$$
 * $$\left(±1,\,±1,\,±3\frac{\sqrt5-1}{2},\,±\frac{3\sqrt5-5}{2}\right),$$
 * $$\left(±\frac32,\,±\frac32,\,±\frac{5-2\sqrt5}{2},\,±\frac{7-2\sqrt5}{2}\right),$$
 * $$\left(±(3-\sqrt5),\,±(3-\sqrt5),\,±1,\,±2\right),$$
 * $$\left(±\frac{3\sqrt5-4}{2},\,±\frac{3\sqrt5-4}{2},\,±\frac12,\,±\frac32\right),$$
 * $$\left(±\frac{3+\sqrt5}{4},\,±\frac12,\,±(4-\sqrt5),\,±\frac{5\sqrt5-7}{4}\right),$$
 * $$\left(±\frac{3+\sqrt5}{4},\,±\frac12,\,±\frac{7-3\sqrt5}{2},\,±\frac{5\sqrt5-3}{4}\right),$$
 * $$\left(±\frac{3+\sqrt5}{4},\,±\frac12,\,±(2\sqrt5-3),\,±\frac{3\sqrt5-1}{4}\right),$$
 * $$\left(±\frac{3+\sqrt5}{4},\,±1,\,±\frac{7\sqrt5-13}{4},\,±\frac{2\sqrt5-1}{2}\right),$$
 * $$\left(±\frac{3+\sqrt5}{4},\,±\frac{3-\sqrt5}{4},\,±\frac32,\,±(2\sqrt5-3)\right),$$
 * $$\left(±\frac{3+\sqrt5}{4},\,±2,\,±\frac{7\sqrt5-13}{4},\,±\frac{\sqrt5-2}{2}\right),$$
 * $$\left(±\frac{3+\sqrt5}{4},\,±\frac{3-\sqrt5}{2},\,±\frac{13-3\sqrt5}{4},\,±\frac{3\sqrt5-4}{2}\right),$$
 * $$\left(±\frac{3+\sqrt5}{4},\,±\frac{3\sqrt5-5}{4},\,±\frac{6-\sqrt5}{2},\,±\frac{3\sqrt5-5}{2}\right),$$
 * $$\left(±\frac{3+\sqrt5}{4},\,±\frac{5-\sqrt5}{2},\,±\frac{13-3\sqrt5}{4},\,±\frac{5-2\sqrt5}{2}\right),$$
 * $$\left(±\frac{3+\sqrt5}{4},\,±3\frac{3-\sqrt5}{4},\,±\frac{6-\sqrt5}{2},\,±(3-\sqrt5)\right),$$
 * $$\left(±\frac12,\,±\frac{1+\sqrt5}{2},\,±5\frac{\sqrt5-1}{4},\,±5\frac{3-\sqrt5}{4}\right),$$
 * $$\left(±\frac12,\,±\frac{5+\sqrt5}{4},\,±(2\sqrt5-3),\,±\frac{5-\sqrt5}{4}\right),$$
 * $$\left(±\frac12,\,±\frac{7+\sqrt5}{4},\,±\frac{5\sqrt5-11}{4},\,±(3-\sqrt5)\right),$$
 * $$\left(±\frac12,\,±\frac{7+\sqrt5}{4},\,±\frac{7\sqrt5-13}{4},\,±\frac{3-\sqrt5}{2}\right),$$
 * $$\left(±\frac12,\,±\frac{3-\sqrt5}{4},\,±(2\sqrt5-3),\,±\frac{1+3\sqrt5}{4}\right),$$
 * $$\left(±\frac12,\,±\frac{5-\sqrt5}{4},\,±\frac{7\sqrt5-13}{4},\,±\sqrt5\right),$$
 * $$\left(±\frac12,\,±\frac{\sqrt5-2}{2},\,±\frac{4-\sqrt5}{2},\,±\frac{9-2\sqrt5}{2}\right),$$
 * $$\left(±\frac12,\,±\sqrt5,\,±\frac{7-3\sqrt5}{4},\,±5\frac{3-\sqrt5}{4}\right),$$
 * $$\left(±\frac12,\,±\frac{9-\sqrt5}{4},\,±\frac{13-3\sqrt5}{4},\,±(3-\sqrt5)\right),$$
 * $$\left(±\frac12,\,±\frac{4-\sqrt5}{2},\,±\frac{6-\sqrt5}{2},\,±\frac{7-2\sqrt5}{2}\right),$$
 * $$\left(±\frac12,\,±\frac{7-3\sqrt5}{4},\,±\frac{13-3\sqrt5}{4},\,±3\frac{\sqrt5-1}{2}\right),$$
 * $$\left(±\frac12,\,±\frac{2\sqrt5-3}{2},\,±\frac{6-\sqrt5}{2},\,±\frac{3\sqrt5-4}{2}\right),$$
 * $$\left(±\frac{1+\sqrt5}{2},\,±1,\,±(2\sqrt5-3),\,±\frac{\sqrt5-1}{2}\right),$$
 * $$\left(±\frac{1+\sqrt5}{2},\,±\frac32,\,±\frac{7\sqrt5-13}{4},\,±3\frac{\sqrt5-1}{4}\right),$$
 * $$\left(±\frac{1+\sqrt5}{2},\,±\frac{4-\sqrt5}{2},\,±\frac{13-3\sqrt5}{4},\,±\frac{5\sqrt5-9}{4}\right),$$
 * $$\left(±\frac{1+\sqrt5}{2},\,±\frac{7-3\sqrt5}{4},\,±\frac{6-\sqrt5}{2},\,±\frac{5\sqrt5-11}{4}\right),$$
 * $$\left(±\frac{5+\sqrt5}{4},\,±1,\,±\frac{7-2\sqrt5}{2},\,±\frac{5\sqrt5-9}{4}\right),$$
 * $$\left(±\frac{5+\sqrt5}{4},\,±\frac{5-\sqrt5}{4},\,±(3-\sqrt5),\,±\frac{3\sqrt5-4}{2}\right),$$
 * $$\left(±\frac{5+\sqrt5}{4},\,±\frac{\sqrt5-2}{2},\,±\frac{9-\sqrt5}{4},\,±\frac{7-3\sqrt5}{2}\right),$$
 * $$\left(±\frac{5+\sqrt5}{4},\,±3\frac{\sqrt5-1}{4},\,±\frac{5-\sqrt5}{2},\,±3\frac{\sqrt5-2}{2}\right),$$
 * $$\left(±1,\,±\frac{3-\sqrt5}{4},\,±\frac{7-3\sqrt5}{4},\,±\frac{9-2\sqrt5}{2}\right),$$
 * $$\left(±1,\,±\frac{1+3\sqrt5}{4},\,±\frac{2\sqrt5-3}{2},\,±5\frac{3-\sqrt5}{4}\right),$$
 * $$\left(±1,\,±\sqrt5,\,±\frac{3-\sqrt5}{2},\,±\frac{7-3\sqrt5}{2}\right),$$
 * $$\left(±1,\,±\frac{3-\sqrt5}{2},\,±\frac{5-\sqrt5}{2},\,±(4-\sqrt5)\right),$$
 * $$\left(±\frac{7+\sqrt5}{4},\,±\frac{3-\sqrt5}{4},\,±\frac{4-\sqrt5}{2},\,±\frac{7-3\sqrt5}{2}\right),$$
 * $$\left(±\frac{7+\sqrt5}{4},\,±\frac{3-\sqrt5}{4},\,±\frac{5-2\sqrt5}{2},\,±\frac{3\sqrt5-5}{2}\right),$$
 * $$\left(±\frac{7+\sqrt5}{4},\,±\frac{\sqrt5-1}{2},\,±3\frac{3-\sqrt5}{4},\,±3\frac{\sqrt5-2}{2}\right),$$
 * $$\left(±\frac{3-\sqrt5}{4},\,±3\frac{\sqrt5-1}{4},\,±\frac{3-\sqrt5}{2},\,±\frac{9-2\sqrt5}{2}\right),$$
 * $$\left(±\frac{3-\sqrt5}{4},\,±\frac{2\sqrt5-1}{2},\,±\frac{7-3\sqrt5}{4},\,±(4-\sqrt5)\right),$$
 * $$\left(±\frac{3-\sqrt5}{4},\,±\frac{5-\sqrt5}{2},\,±\frac{3\sqrt5-4}{2},\,±5\frac{\sqrt5-1}{4}\right),$$
 * $$\left(±\frac{3-\sqrt5}{4},\,±2,\,±\frac{3\sqrt5-4}{2},\,±\frac{5\sqrt5-9}{4}\right),$$
 * $$\left(±\frac{3-\sqrt5}{4},\,±\frac{7-3\sqrt5}{4},\,±(3-\sqrt5),\,±\frac{3\sqrt5-2}{2}\right),$$
 * $$\left(±\frac{1+3\sqrt5}{4},\,±\frac32,\,±\frac{7-3\sqrt5}{2},\,±\frac{3\sqrt5-5}{4}\right),$$
 * $$\left(±\frac{1+3\sqrt5}{4},\,±\frac{4-\sqrt5}{2},\,±(3-\sqrt5),\,±\frac{5\sqrt5-7}{4}\right),$$
 * $$\left(±\frac{1+3\sqrt5}{4},\,±\frac{5-\sqrt5}{2},\,±\frac{5\sqrt5-11}{4},\,±\frac{2\sqrt5-3}{2}\right),$$
 * $$\left(±\frac32,\,±\frac{5-\sqrt5}{4},\,±3\frac{3-\sqrt5}{4},\,±(4-\sqrt5)\right),$$
 * $$\left(±\frac32,\,±\frac{5-\sqrt5}{4},\,±\frac{5\sqrt5-11}{4},\,±3\frac{\sqrt5-1}{2}\right),$$
 * $$\left(±\frac32,\,±\frac{3-\sqrt5}{2},\,±\frac{9-\sqrt5}{4},\,±5\frac{3-\sqrt5}{4}\right),$$
 * $$\left(±\frac32,\,±\frac{2\sqrt5-1}{2},\,±\frac{4-\sqrt5}{2},\,±3\frac{\sqrt5-2}{2}\right),$$
 * $$\left(±\frac{\sqrt5-1}{2},\,±\frac{5-\sqrt5}{4},\,±\frac{9-2\sqrt5}{2},\,±\frac{3\sqrt5-5}{4}\right),$$
 * $$\left(±\frac{\sqrt5-1}{2},\,±\frac{9-\sqrt5}{4},\,±\frac{3\sqrt5-4}{2},\,±\frac{5\sqrt5-7}{4}\right),$$
 * $$\left(±\frac{\sqrt5-1}{2},\,±\frac{7-3\sqrt5}{4},\,±\frac{7-2\sqrt5}{2},\,±\frac{5\sqrt5-3}{4}\right),$$
 * $$\left(±\frac{5-\sqrt5}{4},\,±\frac{3\sqrt5-1}{4},\,±\frac{2\sqrt5-3}{2},\,±(4-\sqrt5)\right),$$
 * $$\left(±\frac{5-\sqrt5}{4},\,±2,\,±5\frac{3-\sqrt5}{4},\,±\frac{4-\sqrt5}{2}\right),$$
 * $$\left(±\frac{5-\sqrt5}{4},\,±\frac{3-\sqrt5}{2},\,±\frac{5\sqrt5-11}{4},\,±\frac{3\sqrt5-2}{2}\right),$$
 * $$\left(±\frac{5-\sqrt5}{4},\,±\frac{4-\sqrt5}{2},\,±\frac{3\sqrt5-5}{2},\,±\frac{5\sqrt5-3}{4}\right),$$
 * $$\left(±\frac{3\sqrt5-1}{4},\,±2,\,±3\frac{\sqrt5-2}{2},\,±\frac{7-3\sqrt5}{4}\right),$$
 * $$\left(±\frac{3\sqrt5-1}{4},\,±\frac{3-\sqrt5}{2},\,±\frac{7-2\sqrt5}{2},\,±5\frac{\sqrt5-1}{4}\right),$$
 * $$\left(±\frac{3\sqrt5-1}{4},\,±\frac{9-\sqrt5}{4},\,±\frac{3\sqrt5-5}{2},\,±\frac{2\sqrt5-3}{2}\right),$$
 * $$\left(±\frac{2-\sqrt5}{2},\,±\frac{2\sqrt5-3}{2},\,±\frac{5-2\sqrt5}{2},\,±\frac{3\sqrt5-2}{2}\right),$$
 * $$\left(±\frac{\sqrt5-2}{2},\,±3\frac{3-\sqrt5}{4},\,±3\frac{\sqrt5-1}{2},\,±5\frac{\sqrt5-1}{4}\right),$$
 * $$\left(±\sqrt5,\,±\frac{7-3\sqrt5}{4},\,±\frac{5-2\sqrt5}{2},\,±\frac{5\sqrt5-7}{4}\right),$$
 * $$\left(±\sqrt5,\,±\frac{2\sqrt5-3}{2},\,±3\frac{3-\sqrt5}{4},\,±\frac{5\sqrt5-9}{4}\right),$$
 * $$\left(±3\frac{\sqrt5-1}{4},\,±\frac{4-\sqrt5}{2},\,±3\frac{\sqrt5-1}{2},\,±\frac{5\sqrt5-7}{4}\right),$$
 * $$\left(±3\frac{\sqrt5-1}{4},\,±\frac{5\sqrt5-3}{4},\,±\frac{2\sqrt5-3}{2},\,±(3-\sqrt5)\right),$$
 * $$\left(±\frac{3-\sqrt5}{2},\,±\frac{3\sqrt5-5}{4},\,±\frac{5\sqrt5-9}{4},\,±\frac{3\sqrt5-2}{2}\right),$$
 * $$\left(±\frac{3-\sqrt5}{2},\,±\frac{7-3\sqrt5}{4},\,±\frac{3\sqrt5-4}{2},\,±\frac{5\sqrt5-3}{4}\right),$$
 * $$\left(±\frac{2\sqrt5-1}{2},\,±\frac{3\sqrt5-5}{4},\,±(3-\sqrt5),\,±5\frac{\sqrt5-1}{4}\right),$$
 * $$\left(±\frac{2\sqrt5-1}{2},\,±\frac{4-\sqrt5}{2},\,±\frac{3\sqrt5-4}{2},\,±\frac{2\sqrt5-3}{2}\right).$$