Dishecatonicosatruncated prismatodishecatonicosachoron

The dishecatonicositruncated prismatodishecatonicosachoron, or dohitipady, is a nonconvex uniform polychoron that consists of 1200 hexagonal prisms, 120 great rhombicosidodecahedra, 120 great quasitruncated icosidodecahedra, and 120 icosidodecatruncated icosidodecahedra. 1 of each type of cell join at each vertex.

Vertex coordinates
Vertex coordinates for a dishecatonicositruncated prismatodishecatonicosachoron of edge length 1 are given by all permutations of: plus all even permutations of:
 * $$\left(±\frac12,\,±\frac12,\,±\frac{2\sqrt5-3}{2},\,±\frac{2+3\sqrt5}{2}\right),$$
 * $$\left(±\frac12,\,±\frac12,\,±\frac{3\sqrt5-2}{2},\,±\frac{3+2\sqrt5}{2}\right),$$
 * $$\left(±\frac{5-\sqrt5}{4},\,±\frac{5-\sqrt5}{4},\,±\frac{5\sqrt5-1}{4},\,±\frac{3+5\sqrt5}{4}\right),$$
 * $$\left(±\frac{5+\sqrt5}{4},\,±\frac{5+\sqrt5}{4},\,±\frac{5\sqrt5-3}{4},\,±\frac{1+5\sqrt5}{4}\right),$$
 * $$\left(±\frac{5\sqrt5-1}{4},\,±\frac{5\sqrt5-1}{4},\,±\frac{3+\sqrt5}{4},\,±\frac{7+\sqrt5}{4}\right),$$
 * $$\left(±\frac{1+5\sqrt5}{4},\,±\frac{1+\sqrt5}{4},\,±\frac{3-\sqrt5}{4},\,±\frac{7-\sqrt5}{4}\right),$$
 * $$\left(±\frac{7-3\sqrt5}{4},\,±\frac{3-\sqrt5}{4},\,±1,\,±\frac{2+3\sqrt5}{2}\right),$$
 * $$\left(±\frac{7-3\sqrt5}{4},\,±\frac{5-\sqrt5}{4},\,±\frac{11+\sqrt5}{4},\,±\frac{5+3\sqrt5}{4}\right),$$
 * $$\left(±\frac{7-3\sqrt5}{4},\,±1,\,±\frac{4+\sqrt5}{2},\,±\frac{1+5\sqrt5}{4}\right),$$
 * $$\left(±\frac{7-3\sqrt5}{4},\,±\frac{3+\sqrt5}{4},\,±\frac{9-\sqrt5}{4},\,±3\frac{3+\sqrt5}{4}\right),$$
 * $$\left(±\frac{7-3\sqrt5}{4},\,±\frac{3\sqrt5-1}{4},\,±2,\,±\frac{3+2\sqrt5}{2}\right),$$
 * $$\left(±\frac{\sqrt5-2}{2},\,±\frac12,\,±\frac{4-\sqrt5}{2},\,±\frac{2+3\sqrt5}{2}\right),$$
 * $$\left(±\frac{\sqrt5-2}{2},\,±\frac12,\,±\frac72,\,±\frac{1+2\sqrt5}{2}\right),$$
 * $$\left(±\frac{\sqrt5-2}{2},\,±\frac{3+\sqrt5}{4},\,±\frac{5-\sqrt5}{2},\,±5\frac{1+\sqrt5}{4}\right),$$
 * $$\left(±\frac{\sqrt5-2}{2},\,±\frac{3+\sqrt5}{4},\,±3,\,±\frac{1+5\sqrt5}{4}\right),$$
 * $$\left(±\frac{\sqrt5-2}{2},\,±\frac{1+\sqrt5}{2},\,±\frac{11-\sqrt5}{4},\,±\frac{3+5\sqrt5}{4}\right),$$
 * $$\left(±\frac{3-\sqrt5}{4},\,±\frac{3-\sqrt5}{2},\,±3\frac{\sqrt5-1}{4},\,±\frac{2+3\sqrt5}{2}\right),$$
 * $$\left(±\frac{3-\sqrt5}{4},\,±\frac12,\,±4,\,±\frac{1+3\sqrt5}{4}\right),$$
 * $$\left(±\frac{3-\sqrt5}{4},\,±3\frac{3-\sqrt5}{4},\,±\frac{7+3\sqrt5}{4},\,±\frac{9+\sqrt5}{4}\right),$$
 * $$\left(±\frac{3-\sqrt5}{4},\,±3\frac{3-\sqrt5}{4},\,±5\frac{1+\sqrt5}{4},\,±\frac{5+\sqrt5}{4}\right),$$
 * $$\left(±\frac{3-\sqrt5}{4},\,±\frac{3+\sqrt5}{4},\,±\frac32,\,±4\right),$$
 * $$\left(±\frac{3-\sqrt5}{4},\,±5\frac{\sqrt5-1}{4},\,±\frac{2+\sqrt5}{2},\,±\frac{5+\sqrt5}{2}\right),$$
 * $$\left(±\frac{3-\sqrt5}{4},\,±\frac{2+\sqrt5}{2},\,±3,\,±\frac{5\sqrt5-1}{4}\right),$$
 * $$\left(±\frac{3-\sqrt5}{4},\,±\frac{11-\sqrt5}{4},\,±\frac{1+5\sqrt5}{4},\,±3\frac{1+\sqrt5}{4}\right),$$
 * $$\left(±\frac{3-\sqrt5}{2},\,±\frac12,\,±3\frac{3+\sqrt5}{4},\,±\frac{5\sqrt5-3}{4}\right),$$
 * $$\left(±\frac{3-\sqrt5}{2},\,±\frac{5-\sqrt5}{4},\,±5\frac{1+\sqrt5}{4},\,±\frac{2\sqrt5-1}{2}\right),$$
 * $$\left(±\frac{3-\sqrt5}{2},\,±2,\,±3,\,±\frac{3+\sqrt5}{2}\right),$$
 * $$\left(±\frac{3-\sqrt5}{2},\,±\frac{11-\sqrt5}{4},\,±\frac{4+\sqrt5}{2},\,±\frac{7+\sqrt5}{4}\right),$$
 * $$\left(±\frac{3\sqrt5-5}{4},\,±\frac12,\,±\frac{5+\sqrt5}{2}<\,±\frac{5\sqrt5-1}{4}\right),$$
 * $$\left(±\frac{3\sqrt5-5}{4},\,±\frac{\sqrt5-1}{2},\,±\frac{5-\sqrt5}{4},\,±\frac{2+3\sqrt5}{2}\right),$$
 * $$\left(±\frac{3\sqrt5-5}{4},\,±\frac{7-\sqrt5}{4},\,±5\frac{1+\sqrt5}{4},\,±\frac{3\sqrt5-1}{4}\right),$$
 * $$\left(±\frac{3\sqrt5-5}{4},\,±\frac32,\,±3,\,±\frac{5+3\sqrt5}{4}\right),$$
 * $$\left(±\frac{3\sqrt5-5}{4},\,±\frac{5+\sqrt5}{4},\,±\frac{11-\sqrt5}{4},\,±\frac{7+3\sqrt5}{4}\right),$$
 * $$\left(±\frac12,\,±3\frac{3-\sqrt5}{4},\,±\frac{3+5\sqrt5}{4},\,±\frac{3+\sqrt5}{2}\right),$$
 * $$\left(±\frac12,\,±3\frac{3-\sqrt5}{4},\,±3\frac{3+\sqrt5}{4},\,±2\right),$$
 * $$\left(±\frac12,\,±\frac{5-\sqrt5}{4},\,±4,\,±\frac{5+\sqrt5}{4}\right),$$
 * $$\left(±\frac12,\,±1,\,±5\frac{1+\sqrt5}{4},\,±5\frac{\sqrt5-1}{4}\right),$$
 * $$\left(±\frac12,\,±\frac{3+\sqrt5}{4},\,±4,\,±\frac{3\sqrt5-1}{4}\right),$$
 * $$\left(±\frac12,\,±\frac{5-\sqrt5}{2},\,±\frac{1+5\sqrt5}{4},\,±\frac{5+3\sqrt5}{4}\right),$$
 * $$\left(±\frac12,\,±\frac{9-\sqrt5}{4},\,±3,\,±\frac{9+\sqrt5}{4}\right),$$
 * $$\left(±\frac12,\,±\frac{2\sqrt5-1}{2},\,±\frac{2+\sqrt5}{2},\,±\frac72\right),$$
 * $$\left(±\frac12,\,±2,\,±\frac{1+5\sqrt5}{4},\,±\frac{5\sqrt5-1}{4}\right),$$
 * $$\left(±\frac12,\,±2,\,±\frac{11-\sqrt5}{4},\,±\frac{11+\sqrt5}{4}\right),$$
 * $$\left(±\frac12,\,±\frac{2+\sqrt5}{2},\,±\frac{4+\sqrt5}{2},\,±\frac{3\sqrt5-2}{2}\right),$$
 * $$\left(±3\frac{3-\sqrt5}{4},\,±\frac{\sqrt5-1}{2},\,±\frac{7+\sqrt5}{4},\,±\frac{3+2\sqrt5}{2}\right),$$
 * $$\left(±\frac{\sqrt5-1}{2},\,±1,\,±4,\,±\frac{1+\sqrt5}{2}\right),$$
 * $$\left(±\frac{\sqrt5-1}{2},\,±\frac{9-\sqrt5}{4},\,±\frac{1+5\sqrt5}{4},\,±\frac{1+2\sqrt5}{2}\right),$$
 * $$\left(±\frac{\sqrt5-1}{2},\,±\frac{5\sqrt5-3}{4},\,±\frac{2+\sqrt5}{2},\,±\frac{11+\sqrt5}{4}\right),$$
 * $$\left(±\frac{5-\sqrt5}{4},\,±\frac{2\sqrt5-3}{2},\,±3\frac{1+\sqrt5}{4},\,±\frac{5+\sqrt5}{2}\right),$$
 * $$\left(±\frac{5-\sqrt5}{4},\,±\frac{3+\sqrt5}{4},\,±3\frac{3+\sqrt5}{4},\,±5\frac{\sqrt5-1}{4}\right),$$
 * $$\left(±\frac{5-\sqrt5}{4},\,±\frac{5-\sqrt5}{2},\,±\frac{4+\sqrt5}{2},\,±\frac{9+\sqrt5}{4}\right),$$
 * $$\left(±\frac{5-\sqrt5}{4},\,±\frac{5+\sqrt5}{4},\,±2,\,±\frac72\right),$$
 * $$\left(±\frac{2\sqrt5-3}{2},\,±\frac{7-\sqrt5}{4},\,±3\frac{3+\sqrt5}{4},\,±\frac{1+\sqrt5}{2}\right),$$
 * $$\left(±\frac{2\sqrt5-3}{2},\,±\frac32,\,±\frac{4+\sqrt5}{2},\,±\frac{1+2\sqrt5}{2}\right),$$
 * $$\left(±\frac{2\sqrt5-3}{2},\,±\frac{1+3\sqrt5}{4},\,±2,\,±\frac{7+3\sqrt5}{4}\right),$$
 * $$\left(±\frac{4-\sqrt5}{2},\,±1,\,±\frac{7+3\sqrt5}{4},\,±\frac{5\sqrt5-1}{4}\right),$$
 * $$\left(±\frac{4-\sqrt5}{2},\,±\frac{7-\sqrt5}{4},\,±\frac{11+\sqrt5}{4},\,±\frac{3+\sqrt5}{2}\right),$$
 * $$\left(±\frac{4-\sqrt5}{2},\,±\frac32,\,±\frac{3+2\sqrt5}{2},\,±\frac{2\sqrt5-1}{2}\right),$$
 * $$\left(±\frac{4-\sqrt5}{2},\,±\frac{9-\sqrt5}{4},\,±\frac{5+\sqrt5}{2},\,±\frac{5+\sqrt5}{4}\right),$$
 * $$\left(±3\frac{\sqrt5-1}{4},\,±1,\,±\frac72,\,±3\frac{1+\sqrt5}{4}\right),$$
 * $$\left(±3\frac{\sqrt5-1}{4},\,±\frac{3+\sqrt5}{4},\,±\frac{11+\sqrt5}{4},\,±\frac{5\sqrt5-1}{4}\right),$$
 * $$\left(±3\frac{\sqrt5-1}{4},\,±\frac{5-\sqrt5}{2},\,±\frac{3+2\sqrt5}{2},\,±\frac{5+\sqrt5}{4}\right),$$
 * $$\left(±3\frac{\sqrt5-1}{4},\,±\frac{9-\sqrt5}{4},\,±\frac{3+5\sqrt5}{4},\,±\frac{1+3\sqrt5}{4}\right),$$
 * $$\left(±1,\,±\frac{7-\sqrt5}{4},\,±\frac72,\,±\frac{7+\sqrt5}{4}\right),$$
 * $$\left(±1,\,±\frac{3+\sqrt5}{4},\,±\frac{7+3\sqrt5}{4},\,±\frac{3\sqrt5-2}{2}\right),$$
 * $$\left(±1,\,±\frac{5-\sqrt5}{2},\,±\frac{5+\sqrt5}{2},\,±2\right),$$
 * $$\left(±1,\,±\frac32,\,±\frac{3+5\sqrt5}{4},\,±\frac{5\sqrt5-3}{4}\right),$$
 * $$\left(±\frac{3+\sqrt5}{4},\,±\frac{3\sqrt5-2}{2},\,±3\frac{1+\sqrt5}{4},\,±\frac{3+\sqrt5}{2}\right),$$
 * $$\left(±\frac{3\sqrt5-1}{4},\,±2,\,±\frac{5\sqrt5-1}{4},\,±\frac{1+2\sqrt5}{2}\right),$$
 * $$\left(±\frac{3\sqrt5-1}{4},\,±\frac{5\sqrt5-3}{4},\,±3\frac{1+\sqrt5}{4},\,±\frac{9+\sqrt5}{4}\right),$$
 * $$\left(±5\frac{\sqrt5-1}{4},\,±\frac{5+\sqrt5}{4},\,±\frac{3+\sqrt5}{2},\,±\frac{1+2\sqrt5}{2}\right),$$
 * $$\left(±5\frac{\sqrt5-1}{4},\,±\frac{1+3\sqrt5}{4},\,±\frac{7+\sqrt5}{4},\,±\frac{5+3\sqrt5}{4}\right),$$
 * $$\left(±\frac{1+\sqrt5}{2},\,±\frac{2\sqrt5-1}{2},\,±\frac{5\sqrt5-1}{4},\,±\frac{9+\sqrt5}{2}\right),$$
 * $$\left(±\frac{1+\sqrt5}{2},\,±\frac{5+\sqrt5}{4},\,±\frac{3\sqrt5-2}{2},\,±\frac{5+3\sqrt5}{4}\right),$$
 * $$\left(±\frac{2\sqrt5-1}{2},\,±\frac{1+3\sqrt5}{4},\,±2,\,±\frac{1+5\sqrt5}{2}\right),$$