Great dishecatonicosaquasitruncated prismatodishecatonicosachoron

The great dishecatonicosiquasitruncated prismatodishecatonicosachoron, or gidhiquit paddy, is a nonconvex uniform polychoron that consists of 720 decagrammic prisms, 120 great quasitruncated icosidodecahedra, 120 quasitruncated dodecadodecahedra, and 120 icosidodecatruncated icosidodecahedra. 1 of each type of cell join at each vertex.

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