Hexacositrishecatonicosachoron

The hexacositrishecatonicosachoron, or xithi, is a nonconvex uniform polychoron that consists of 600 truncated octahedra, 120 quasitruncated dodecadodecahedra, 120 great rhombicosidodecahedra, and 120 great quasitruncated icosidodecahedra. 1 of each type of cell join at each vertex.

Vertex coordinates
Vertex coordinates for a great disprismatohexacosihecatonicosachoron of edge length 1 are given by all permutations of: *$$\left(±\frac12,\,±\frac12,\,±\frac{2\sqrt5-3}{2},\,±\frac{3+2\sqrt5}{2}\right),$$ plus all even permutations of:
 * $$\left(±\frac12,\,±\frac12,\,±\frac32,\,±\frac72\right),$$
 * $$\left(±1,\,±1,\,±2,\,±3\right),$$
 * $$\left(±\frac{\sqrt5}{2},\,±\frac{\sqrt5}{2},\,±\frac12,\,±\frac72\right),$$
 * $$\left(±\frac32,\,±\frac32,\,±\frac{4-\sqrt5}{2},\,±\frac{4+\sqrt5}{2}\right),$$
 * $$\left(±\frac32,\,±\frac32,\,±\frac{2\sqrt5-1}{2},\,±\frac{1+2\sqrt5}{2}\right),$$
 * $$\left(±2,\,±2,\,±\frac{3-\sqrt5}{2},\,±\frac{3+\sqrt5}{2}\right),$$
 * $$\left(±\sqrt5,\,±\sqrt5,\,±1,\,±2\right),$$
 * $$\left(±\frac52,\,±\frac52,\,±\frac12,\,±\frac32\right),$$
 * $$\left(±\frac{7-3\sqrt5}{4},\,±\frac{3-\sqrt5}{4},\,±1,\,±\frac{3+2\sqrt5}{2}\right),$$
 * $$\left(±\frac{7-3\sqrt5}{4},\,±\frac12,\,±\frac{9+\sqrt5}{4},\,±\frac{3+\sqrt5}{2}\right),$$
 * $$\left(±\frac{7-3\sqrt5}{4},\,±\frac{1+\sqrt5}{4},\,±\frac{3+\sqrt5}{2},\,±\frac{1+2\sqrt5}{2}\right),$$
 * $$\left(±\frac{7-3\sqrt5}{4},\,±1,\,±\frac32,\,±\frac{7+3\sqrt5}{4}\right),$$
 * $$\left(±\frac{7-3\sqrt5}{4},\,±\frac{\sqrt5}{2},\,±\frac{5+\sqrt5}{4},\,±(1+\sqrt5)\right),$$
 * $$\left(±\frac{\sqrt5-2}{2},\,±\frac{\sqrt5-1}{4},\,±3,\,±3\frac{1+\sqrt5}{4}\right),$$
 * $$\left(±\frac{\sqrt5-2}{2},\,±\frac12,\,±\frac{4-\sqrt5}{2},\,±\frac{3+2\sqrt5}{2}\right),$$
 * $$\left(±\frac{\sqrt5-2}{2},\,±1,\,±\frac{7-\sqrt5}{4},\,±\frac{3+5\sqrt5}{4}\right),$$
 * $$\left(±\frac{\sqrt5-2}{2},\,±\frac{\sqrt5}{2},\,±\frac52,\,±\frac{1+2\sqrt5}{2}\right),$$
 * $$\left(±\frac{\sqrt5-2}{2},\,±\frac{3+\sqrt5}{4},\,±2,\,±\frac{1+5\sqrt5}{4}\right),$$
 * $$\left(±\frac{3-\sqrt5}{4},\,±\frac{\sqrt5-1}{4},\,±\frac72,\,±\frac{1+\sqrt5}{2}\right),$$
 * $$\left(±\frac{3-\sqrt5}{4},\,±\frac{3-\sqrt5}{2},\,±3\frac{\sqrt5-1}{4},\,±\frac{3+2\sqrt5}{2}\right),$$
 * $$\left(±\frac{3-\sqrt5}{4},\,±\frac{3-\sqrt5}{2},\,±\frac{5+3\sqrt5}{4},\,±\frac52\right),$$
 * $$\left(±\frac{3-\sqrt5}{4},\,±\frac{3-\sqrt5}{2},\,±\frac{3+5\sqrt5}{4},\,±\frac32\right),$$
 * $$\left(±\frac{3-\sqrt5}{4},\,±1,\,±\frac{5\sqrt5-1}{4},\,±\frac{1+2\sqrt5}{2}|right),$$
 * $$\left(±\frac{3-\sqrt5}{4},\,±(\sqrt5-1),\,±\frac{1+3\sqrt5}{4},\,±\frac{4+\sqrt5}{2}\right),$$
 * $$\left(±\frac{3-\sqrt5}{4},\,±1,\,±\frac{3+\sqrt5}{4},\,±\frac72\right),$$
 * $$\left(±\frac{3-\sqrt5}{4},\,±\frac{1+3\sqrt5}{4},\,±\frac52,\,±\sqrt5\right),$$
 * $$\left(±\frac{3-\sqrt5}{4},\,±2,\,±\frac{5\sqrt5-1}{4},\,±\frac{2+\sqrt5}{2}\right),$$
 * $$\left(±\frac{\sqrt5-1}{4},\,±\frac{3-\sqrt5}{2},\,±\frac{2\sqrt5-1}{2},\,±\frac{7+3\sqrt5}{4}\right),$$
 * $$\left(±\frac{\sqrt5-1}{4},\,±\frac{3\sqrt5-5}{4},\,±\sqrt5,\,±\frac{4+\sqrt5}{2}\right),$$
 * $$\left(±\frac{\sqrt5-1}{4},\,±\frac12,\,±\frac{5\sqrt5-3}{4},\,±(1+\sqrt5)\right),$$
 * $$\left(±\frac{3-\sqrt5}{2},\,±\frac12,\,±\frac{9-\sqrt5}{4},\,±\frac{7+3\sqrt5}{4}\right),$$
 * $$\left(±\frac{3-\sqrt5}{2},\,±\frac12,\,±\frac{7+\sqrt5}{4},\,±\frac{1+5\sqrt5}{4}\right),$$
 * $$\left(±\frac{3-\sqrt5}{2},\,±\frac12,\,±\frac{3+5\sqrt5}{4},\,±\frac{3\sqrt5-1}{4}\right),$$
 * $$\left(±\frac{3-\sqrt5}{2},\,±\frac{\sqrt5-1}{2},\,±2,\,±(1+\sqrt5)\right),$$
 * $$\left(±\frac{3-\sqrt5}{2},\,±\frac{5+\sqrt5}{4},\,±\frac52,\,±\frac{7+\sqrt5}{4}\right),$$
 * $$\left(±\frac{3\sqrt5-5}{4},\,±\frac{\sqrt5-1}{2},\,±\frac{5-\sqrt5}{4},\,±\frac{3+2\sqrt5}{2}\right),$$
 * $$\left(±\frac{3\sqrt5-5}{4},\,±1,\,±\frac{3+5\sqrt5}{4},\,±\frac{\sqrt5}{2}\right),$$
 * $$\left(±\frac{3\sqrt5-5}{4},\,±\frac{3+\sqrt5}{4},\,±\frac52,\,±\frac{3+\sqrt5}{2}\right),$$
 * $$\left(±\frac{3\sqrt5-5}{4},\,±\frac32,\,±2,\,±\frac{5+3\sqrt5}{4}\right),$$
 * $$\left(±\frac12,\,±\frac{5-\sqrt5}{4},\,±\sqrt5,\,±\frac{1+5\sqrt5}{4}\right),$$
 * $$\left(±\frac12,\,±\frac{2\sqrt5-3}{2},\,±\frac{2+\sqrt5}{2},\,±\frac{4+\sqrt5}{2}\right),$$
 * $$\left(±\frac12,\,±\frac{1+\sqrt5}{4},\,±\frac{3+5\sqrt5}{4},\,±(\sqrt5-1)\right),$$
 * $$\left(±\frac12,\,±\frac{7-\sqrt5}{4},\,±\frac{5\sqrt5-1}{4},\,±\frac{3+\sqrt5}{2}\right),$$
 * $$\left(±\frac12,\,±\frac{3\sqrt5-1}{4},\,±\frac{1+3\sqrt5}{4},\,±3\right),$$
 * $$\left(±\frac12,\,±\frac{9-\sqrt5}{4},\,±2,\,±\frac{9+\sqrt5}{4}\rigt),$$
 * $$\left(±\frac12,\,±\frac{5+\sqrt5}{4},\,±\frac{5\sqrt5-1}{4},\,±\sqrt5\right),$$
 * $$\left(±\frac12,\,±\frac{1+3\sqrt5}{4},\,±\frac{3+\sqrt5}{2},\,±\frac{5\sqrt5-3}{4}\right),$$
 * $$\left(±\frac{\sqrt5-1}{2},\,±\frac{1+\sqrt5}{4},\,±\frac72,\,±\frac{3+\sqrt5}{4}\right),$$
 * $$\left(±\frac{\sqrt5-1}{2},\,±\frac32,\,±\frac{5\sqrt5-1}{4},\,±3\frac{1+\sqrt5}{4}\right),$$
 * $$\left(±\frac{\sqrt5-1}{2},\,±\frac{2\sqrt5-1}{2},\,±\frac{1+3\sqrt5}{4},\,±\frac{9+\sqrt5}{4}\right),$$
 * $$\left(±\frac{5-\sqrt5}{4},\,±\frac{\sqrt5}{2},\,±\frac{7+3\sqrt5}{4},\,±(\sqrt5-1)\right),$$
 * $$\left(±\frac{5-\sqrt5}{4},\,±\frac{7-\sqrt5}{4},\,±\frac{3+\sqrt5}{2},\,±\frac52\right),$$
 * $$\left(±\frac{5-\sqrt5}{4},\,±\frac32,\,±\frac{5+\sqrt5}{4},\,±3\right),$$
 * $$\left(±\frac{2\sqrt5-3}{2},\,±1,\,±\frac{7+3\sqrt5}{4},\,±\frac{3+\sqrt5}{4}\right),$$
 * $$\left(±\frac{2\sqrt5-3}{2},\,±\frac{3+\sqrt5}{4},\,±\frac{3+\sqrt5}{2},\,±3\frac{1+\sqrt5}{4}\right),$$
 * $$\left(±\frac{2\sqrt5-3}{2},\,±\frac{1+\sqrt5}{2},\,±\frac{5+\sqrt5}{4},\,±\frac{5+3\sqrt5}{4}\right),$$
 * $$\left(±\frac{1+\sqrt5}{4},\,±\frac{4-\sqrt5}{2},\,±\sqrt5,\,±\frac{5+3\sqrt5}{4}\right),$$
 * $$\left(±\frac{1+\sqrt5}{4},\,±3\frac{\sqrt5-1}{4},\,±\frac{2+\sqrt5}{2},\,±3\right),$$
 * \left(±\frac{4-\sqrt5}{2},\,±1,\,±\frac{9+\sqrt5}{4},\,±\frac{7+\sqrt5}{4}\right),<?math>
 * $$\left(±\frac{4-\sqrt5}{2},\,±\frac{3+\sqrt5}{4},\,±(1+\sqrt5),\,±\frac{3\sqrt5-1}{4}\right),$$
 * $$\left(±3\frac{\sqrt5-1}{4},\,±\frac{\sqrt5}{2},\,±\frac{9+\sqrt5}{4},\,±\sqrt5\right),$$
 * $$\left(±3\frac{\sqrt5-1}{4},\,±\frac{7-\sqrt5}{4},\,±(1+\sqrt5),\,±\frac32\right),$$
 * $$\left(±3\frac{\sqrt5-1}{4},\,±\frac32,\,±\frac{1+5\sqrt5}{4},\,±1+\sqrt5}{2}\right),$$
 * $$\left(±1,\,±\frac{\sqrt5}{2},\,±\frac{5+3\sqrt5}{4},\,±\frac{5\sqrt5-3}{4}\right),$$
 * $$\left(±1,\,±\frac{3+\sqrt5}{4},\,±\frac{1+5\sqrt5}{4},\,±\frac{2\sqrt5-1}{2}\right),$$
 * $$\left(±1,\,±\frac{7-\sqrt5}{4},\,±\frac{4+\sqrt5}{2},\,±\frac{9-\sqrt5}{4}\right),$$
 * $$\left(±1,\,±\frac{5\sqrt5-3}{4},\,±\frac{2+\sqrt5}{2},\,±\frac{9+\sqrt5}{4}\right),$$
 * $$\left(±\frac{\sqrt5}{2},\,±\frac{9-\sqrt5}{4},\,±\sqrt5,\,±3\frac{1+\sqrt5}{4}\right),$$
 * $$\left(±\frac{\sqrt5}{2},\,±\frac{2\sqrt5-1}{2},\,±\frac{2+\sqrt5}{2},\,±\frac52\right),$$
 * $$\left(±(\sqrt5-1),\,±\frac32,\,±\frac{7+\sqrt5}{4},\,±3\frac{1+\sqrt5}{4}\right),$$
 * $$\left(±(\sqrt5-1),\,±\frac{1+\sqrt5}{2},\,±2,\,±\frac{3+\sqrt5}{2}\right),$$
 * $$\left(±\frac{3+\sqrt5}{4},\,±\frac{3\sqrt5-1}{4},\,±\sqrt5,\,±\frac52\right),$$
 * $$\left(±\frac{3+\sqrt5}{4},\,±\frac32,\,±\frac{5\sqrt5-3}{4},\,±\frac{3+\sqrt5}{2}\right),$$
 * $$\left(±\frac{3\sqrt5-1}{4},\,±\frac{1+\sqrt5}{2},\,±\frac{9-\sqrt5}{4},\,±\frac{1+2\sqrt5}{2}\right).$$