Grand quasidisprismatodishecatonicosachoron

The grand quasidisprismatodishecatonicosachoron, or gaquidipdy, is a nonconvex uniform polychoron that consists of 1200 hexagonal prisms, 720 decagonal prisms, 120 quasitruncated dodecadodecahedra, and 120 great quasitruncated icosidodecahedra. 1 of each type of cell join at each vertex. It is the quasiomnitruncate of the great faceted hexacosichoron and the great grand hecatonicosachoron.

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