Hecatonicosihexacositruncated prismatohecatonicosihexacosichoron

The hecatonicosihexacositruncated prismatohecatonicosihexacosichoron, or hixtaphix, is a nonconvex uniform polychoron that consists of 720 decagrammic prisms, 600 truncated octahedra, 120 great rhombicosidodecahedra, and 120 icosidodecatruncated icosidodecahedra. 1 of each type of cell join at each vertex.

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