Great quasidisprismatohexacosihecatonicosachoron

The great quasidisprismatohexacosihecatonicosachoron, or gaquidapixhi, is a nonconvex uniform polychoron that consists of 1200 hexagonal prisms, 720 decagrammic prisms, 600 truncated octahedra, and 120 great quasitruncated icosidodecahedra. 1 of each type of cell join at each vertex. It is the quasiomnitruncate of the grand hexacosichoron and the great grand stellated hecatonicosachoron.

Vertex coordinates
Vertex coordinates for a great quasidisprismatohexacosihecatonicosachoron of edge length 1 are given by all permutations of: plus all even permutations of:
 * $$\left(±\frac12,\,±\frac12,\,±\frac{3\sqrt5-4}{2},\,±\frac{12-5\sqrt5}{2}\right),$$
 * $$\left(±\frac12,\,±\frac12,\,±\frac{4\sqrt5-7}{2},\,±\frac{11-4\sqrt5}{2}\right),$$
 * $$\left(±\frac12,\,±\frac12,\,±\frac{2\sqrt5-3}{2},\,±\frac{6\sqrt5-11}{2}\right),$$
 * $$\left(±\frac12,\,±\frac32,\,±\frac{9-4\sqrt5}{2},\,±\frac{9-4\sqrt5}{2}\right),$$
 * $$\left(±1,\,±1,\,±2(\sqrt5-2),\,±(5-2\sqrt5)\right),$$
 * $$\left(±\frac{3-\sqrt5}{2},\,±\frac{5-\sqrt5}{2},\,±2(\sqrt5-2),\,±2(\sqrt5-2)\right),$$
 * $$\left(±\frac{4-\sqrt5}{2},\,±\frac{4-\sqrt5}{2},\,±\frac{4\sqrt5-7}{2},\,±\frac{9-4\sqrt5}{2}\right),$$
 * $$\left(±\frac{2\sqrt5-3}{2},\,±\frac{5-2\sqrt5}{2},\,±\frac{4\sqrt5-7}{2},\,±\frac{4\sqrt5-7}{2}\right),$$
 * $$\left(±(\sqrt5-2),\,±(\sqrt5-2),\,±(2\sqrt5-3),\,±2(\sqrt5-2)\right),$$
 * $$\left(±\frac12,\,±5\frac{3-\sqrt5}{4},\,±\frac{7\sqrt5-15}{4},\,±3\frac{3-\sqrt5}{2}\right),$$
 * $$\left(±\frac12,\,±\frac{7-3\sqrt5}{2},\,±\frac{17-7\sqrt5}{4},\,±\frac{17-5\sqrt5}{4}\right),$$
 * $$\left(±\frac12,\,±1,\,±\frac{5\sqrt5-7}{4},\,±\frac{11\sqrt5-23}{4}\right),$$
 * $$\left(±\frac12,\,±\frac{3-\sqrt5}{4},\,±3\frac{7-3\sqrt5}{4},\,±(2\sqrt5-3)\right),$$
 * $$\left(±\frac12,\,±\frac{3-\sqrt5}{4},\,±\frac{25-9\sqrt5}{4},\,±\frac{3\sqrt5-5}{2}\right),$$
 * $$\left(±\frac12,\,±\frac{\sqrt5-1}{2},\,±\frac{23-9\sqrt5}{4},\,±\frac{7\sqrt5-11}{4}\right),$$
 * $$\left(±\frac12,\,±\frac{\sqrt5-2}{2},\,±\frac{6\sqrt5-11}{2},\,±\frac{4-\sqrt5}{2}\right),$$
 * $$\left(±\frac12,\, ±\frac{7-\sqrt5}{4},\,±\frac{9\sqrt5-17}{4},\,±2(\sqrt5-2)\right),$$
 * $$\left(±\frac12,\,±\frac{3\sqrt5-5}{4},\,±\frac{25-9\sqrt5}{4},\,±(3-\sqrt5)\right),$$
 * $$\left(±\frac12,\,±\frac{3\sqrt5-5}{4},\,±\frac{11\sqrt5-23}{4},\,±\frac{5-\sqrt5}{2}\right),$$
 * $$\left(±\frac12,\,±(\sqrt5-1),\,±\frac{23-9\sqrt5}{4},\,±\frac{13-5\sqrt5}{4}\right),$$
 * $$\left(±\frac12,\,±3\frac{3-\sqrt5}{4},\,±\frac{9\sqrt5-17}{4},\,±3\frac{3-\sqrt5}{2}\right),$$
 * $$\left(±\frac12,\,±(\sqrt5-2),\,±\frac{9\sqrt5-19}{4},\,±\frac{17-5\sqrt5}{4}\right),$$
 * $$\left(±1,\,±\frac{3-\sqrt5}{4},\,±\frac{6\sqrt5-11}{2},\,±\frac{7-3\sqrt5}{4}\right),$$
 * $$\left(±1,\,±\frac{5-\sqrt5}{4},\,±\frac{9\sqrt5-19}{4},\,±\frac{4\sqrt5-7}{2}\right),$$
 * $$\left(±1,\,±\frac{\sqrt5-2}{2},\,±\frac{25-9\sqrt5}{4},\,±\frac{5\sqrt5-11}{4}\right),$$
 * $$\left(±1,\,±3\frac{\sqrt5-1}{4},\,±\frac{23-9\sqrt5}{4},\,±3\frac{\sqrt5-2}{2}\right),$$
 * $$\left(±1,\,±\frac{3\sqrt5-5}{4},\,±\frac{12-5\sqrt5}{2},\,±\frac{11-3\sqrt5}{4}\right),$$
 * $$\left(±1,\,±\frac{4-\sqrt5}{2},\,±\frac{9\sqrt5-17}{4},\,±\frac{17-7\sqrt5}{4}\right),$$
 * $$\left(±1,\,±\frac{2\sqrt5-3}{2},\,±3\frac{7-3\sqrt5}{4},\,±5\frac{3-\sqrt5}{4}\right),$$
 * $$\left(±\frac{3-\sqrt5}{4},\,±\frac{13-5\sqrt5}{4},\,±\frac{4\sqrt5-7}{2},\,±3\frac{3-\sqrt5}{2}\right),$$
 * $$\left(±\frac{3-\sqrt5}{4},\,±3\frac{\sqrt5-2}{2},\,±2(\sqrt5-2),\,±\frac{17-5\sqrt5}{4}\right),$$
 * $$\left(±\frac{3-\sqrt5}{4},\,±\frac32,\,±(\sqrt5-2),\,±\frac{11\sqrt5-23}{4}\right),$$
 * $$\left(±\frac{3-\sqrt5}{4},\,±3\frac{\sqrt5-1}{4},\,±\frac{6\sqrt5-11}{2},\,±\frac{3-\sqrt5}{2}\right),$$
 * $$\left(±\frac{3-\sqrt5}{4},\,±\frac{4-\sqrt5}{2},\,±(\sqrt5-1),\,±\frac{11\sqrt5-23}{4}\right),$$
 * $$\left(±\frac{3-\sqrt5}{4},\,±\frac{11-3\sqrt5}{4},\,±\frac{9-4\sqrt5}{2},\,±3\frac{3-\sqrt5}{2}\right),$$
 * $$\left(±\frac{3-\sqrt5}{4},\,±\frac{5-2\sqrt5}{2},\,±(5-2\sqrt5),\,±\frac{17-5\sqrt5}{4}\right),$$
 * $$\left(±\frac32,\,±\frac{\sqrt5-2}{2},\,±\frac{12-5\sqrt5}{2},\,±\frac{5-2\sqrt5}{2}\right),$$
 * $$\left(±\frac32,\,±\frac{3-\sqrt5}{2},\,±\frac{9\sqrt5-19}{4},\,±\frac{7\sqrt5-15}{4}\right),$$
 * $$\left(±\frac32,\,±\frac{3\sqrt5-5}{4},\,±3\frac{7-3\sqrt5}{4},\,±\frac{7-3\sqrt5}{2}\right),$$
 * $$\left(±\frac{\sqrt5-1}{2},\,±(3-\sqrt5),\,±2(\sqrt5-2),\,±3\frac{3-\sqrt5}{2}\right),$$
 * $$\left(±\frac{\sqrt5-1}{2},\,±\frac{5\sqrt5-11}{4},\,±\frac{9-4\sqrt5}{2},\,±\frac{17-5\sqrt5}{4}\right),$$
 * $$\left(±\frac{\sqrt5-1}{2},\,±\frac{5-\sqrt5}{4},\,±\frac{3\sqrt5-5}{4},\,±\frac{6\sqrt5-11}{2}\right),$$
 * $$\left(±\frac{\sqrt5-1}{2},,\,±\frac{7-\sqrt5}{4},\,±\frac{2\sqrt5-3}{2},\,±\frac{11\sqrt5-23}{4}\right),$$
 * $$\left(±\frac{5-\sqrt5}{4},\,±(\sqrt5-1),\,±\frac{12-5\sqrt5}{2},\,±3\frac{3-\sqrt5}{4}\right),$$
 * $$\left(±\frac{5-\sqrt5}{4},\,±\frac{5-\sqrt5}{2},\,±\frac{9-4\sqrt5}{2},\,±\frac{17-7\sqrt5}{4}\right),$$
 * $$\left(±\frac{5-\sqrt5}{4},\,±(\sqrt5-2),\,±\frac{11-4\sqrt5}{2},\,±5\frac{3-\sqrt5}{4}\right),$$
 * $$\left(±\frac{\sqrt5-2}{2},\,±\frac{13-5\sqrt5}{4},\,±(2\sqrt5-3),\,±\frac{17-7\sqrt5}{4}\right),$$
 * $$\left(±\frac{\sqrt5-2}{2},\,±5\frac{3-\sqrt5}{4},\,±\frac{7\sqrt5-11}{4},\,±2(\sqrt5-2)\right),$$
 * $$\left(±\frac{7-\sqrt5}{4},\,±3\frac{\sqrt5-1}{4},\,±\frac{12-5\sqrt5}{2},\,±(\sqrt5-2)\right),$$
 * $$\left(±\frac{7-\sqrt5}{4},\,±\frac{4-\sqrt5}{2},\,±(5-2\sqrt5),\,±\frac{7\sqrt5-15}{4}\right),$$
 * $$\left(±\frac{7-\sqrt5}{4},\,±\frac{7-3\sqrt5}{4},\,±\frac{11-4\sqrt5}{2},\,±\frac{7-3\sqrt5}{2}\right),$$
 * $$\left(±3\frac{\sqrt5-1}{4},\,±(3-\sqrt5),\,±\frac{4\sqrt5-7}{2},\,±\frac{17-7\sqrt5}{4}\right),$$
 * $$\left(±3\frac{\sqrt5-1}{4},\,±\frac{3\sqrt5-5}{2},\,±\frac{9-4\sqrt5}{2},\,±5\frac{3-\sqrt5}{4}\right),$$
 * $$\left(±\frac{3-\sqrt5}{2},\,±\frac{2\sqrt5-3}{2},\,±\frac{25-9\sqrt5}{4},\,±3\frac{3-\sqrt5}{4}\right),$$
 * $$\left(±\frac{3-\sqrt5}{2},\,±\frac{5\sqrt5-7}{4},\,±\frac{11-4\sqrt5}{2},\,±\frac{13-5\sqrt5}{4}\right),$$
 * $$\left(±\frac{3\sqrt5-5}{4},\,±\frac{3\sqrt5-4}{2},\,±(5-2\sqrt5),\,±\frac{13-5\sqrt5}{4}\right),$$
 * $$\left(±\frac{3\sqrt5-5}{4},\,±3\frac{\sqrt5-2}{2},\,±(2\sqrt5-3),\,±\frac{7\sqrt5-15}{4}\right),$$
 * $$\left(±\frac{3\sqrt5-5}{4},\,±\frac{7\sqrt5-11}{4},\,±\frac{4\sqrt5-7}{2},\,±\frac{7-3\sqrt5}{2}\right),$$
 * $$\left(±\frac{3\sqrt5-5}{4},\,±\frac{4-\sqrt5}{2},\,±(\sqrt5-2),\,±\frac{25-9\sqrt5}{4}\right),$$
 * $$\left(±\frac{3\sqrt5-5}{4},\,±\frac{11-3\sqrt5}{4},\,±\frac{4\sqrt5-7}{2},\,±2(\sqrt5-2)\right),$$
 * $$\left(±\frac{4-\sqrt5}{2},\,±\frac{2\sqrt5-3}{2},\,±\frac{11-4\sqrt5}{2},\,±3\frac{\sqrt5-2}{2}\right),$$
 * $$\left(±\frac{4-\sqrt5}{2},\,±(\sqrt5-2),\,±\frac{23-9\sqrt5}{4},\,±\frac{11-3\sqrt5}{4}\right),$$
 * $$\left(±\frac{4-\sqrt5}{2},\,±\frac{5\sqrt5-7}{4},\,±3\frac{7-3\sqrt5}{4},\,±(3-\sqrt5)\right),$$
 * $$\left(±(\sqrt5-1),\,±\frac{5\sqrt5-11}{4},\,±\frac{4\sqrt5-7}{2},\,±\frac{7\sqrt5-15}{4}\right),$$
 * $$\left(±(\sqrt5-1),\,±\frac{3\sqrt5-5}{2},\,±2(\sqrt5-2),\,±\frac{7-3\sqrt5}{2}\right),$$
 * $$\left(±\frac{7-3\sqrt5}{4},\,±(3-\sqrt5),\,±\frac{3\sqrt5-4}{2},\,±\frac{9\sqrt5-19}{4}\right),$$
 * $$\left(±\frac{7-3\sqrt5}{4},\,±\frac{5-\sqrt5}{2},\,±\frac{5-2\sqrt5}{2},\,±\frac{23-9\sqrt5}{4}\right),$$
 * $$\left(±\frac{7-3\sqrt5}{4},\,±3\frac{3-\sqrt5}{4},\,±(2\sqrt5-3),\,±\frac{9-4\sqrt5}{2}\right),$$
 * $$\left(±\frac{5-\sqrt5}{2},\,±\frac{2\sqrt5-3}{2},\,±3\frac{7-3\sqrt5}{4},\,±\frac{5\sqrt5-11}{4}\right),$$
 * $$\left(±\frac{2\sqrt5-3}{2},\,±\frac{3\sqrt5-4}{2},\,±\frac{9-4\sqrt5}{2},\,±3\frac{\sqrt5-2}{2}\right),$$
 * $$\left(±\frac{2\sqrt5-3}{2},\,±3\frac{3-\sqrt5}{4},\,±\frac{7\sqrt5-11}{4},\,±(5-2\sqrt5)\right),$$
 * $$\left(±\frac{2\sqrt5-3}{2},\,±\frac{11-3\sqrt5}{4},\,±\frac{3\sqrt5-5}{2},\,±\frac{9\sqrt5-19}{4}\right),$$
 * $$\left(±(\sqrt5-2),\,±\frac{3\sqrt5-4}{2},\,±\frac{9\sqrt5-17}{4},\,±\frac{5\sqrt5-11}{4}\right),$$
 * $$\left(±(\sqrt5-2),\,±\frac{5\sqrt5-7}{4},\,±\frac{9-4\sqrt5}{2},\,±\frac{7\sqrt5-11}{4}\right),$$
 * $$\left(±\frac{5\sqrt5-7}{4},\,±\frac{5-2\sqrt5}{2},\,±\frac{3\sqrt5-5}{2},\,±\frac{9\sqrt5-17}{4}\right).$$