Dishecatonicosatruncated dishecatonicosachoron

The dishecatonicositruncated dishecatonicosachoron, or dahitady, is a nonconvex uniform polychoron that consists of 120 truncated great dodecahedra, 120 truncated great icosahedra, and 120 icosidodecatruncated icosidodecahedra. 1 truncated great dodecahedron, 1 truncated great icosahedron, and 2 icosidodecatruncated icosidodecahedra join at each vertex.

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