Great quasidisprismatohecatonicosihecatonicosachoron

The great quasidisprismatohecatonicosihecatonicosachoron, or gaquidphihi, is a nonconvex uniform polychoron that consists of 720 decagonal prisms, 720 decagrammic prisms, 120 great rhombicosidodecahedron, and 120 great quasitruncated icosidodecahedra. 1 of each type of cell join at each vertex. It is the quasiomnitruncate of the grand hecatonicosachoron and the great stellated hecatonicosachoron.

Vertex coordinates
Vertex coordinates for a great quasidisprismatohecatonicosihecatonicosachoron of edge length 1 are given by all permutations of: Plus all even permutations of:
 * $$\left(±\frac{3\sqrt5-5}{4},\,±\frac{3\sqrt5-5}{4},\,±3\frac{1+\sqrt5}{4},\,±\frac{7+3\sqrt5}{4}\right),$$
 * $$\left(±\frac12,\,±\frac12,\,±\frac{2\sqrt5-3}{2},\,±\frac{6+\sqrt5}{2}\right),$$
 * $$\left(±\frac12,\,±\frac12,\,±\frac{6-\sqrt5}{2},\,±\frac{3+2\sqrt5}{2}\right),$$
 * $$\left(±\frac12,\,±\frac12,\,±\frac52,\,±\frac{3\sqrt5}{2}\right),$$
 * $$\left(±3\frac{\sqrt5-1}{4},\,±3\frac{\sqrt5-1}{4},\,±\frac{7+\sqrt5}{4},\,±\frac{11+\sqrt5}{4}\right),$$
 * $$\left(±\frac{9-\sqrt5}{4},\,±\frac{9-\sqrt5}{4},\,±\frac{1+3\sqrt5}{4},\,±\frac{5+3\sqrt5}{4}\right),$$
 * $$\left(±3\frac{1+\sqrt5}{4},\,±3\frac{1+\sqrt5}{4},\,±\frac{7-\sqrt5}{4},\,±\frac{11-\sqrt5}{4}\right),$$
 * $$\left(±\frac{5+3\sqrt5}{4},\,±\frac{5+3\sqrt5}{4},\,±\frac{7-3\sqrt5}{4},\,±3\frac{\sqrt5-1}{4}\right),$$
 * $$\left(±\frac{9+\sqrt5}{4},\,±\frac{9+\sqrt5}{4},\,±\frac{3\sqrt5-5}{4},\,±\frac{3\sqrt5-1}{4}\right),$$
 * $$\left(±\frac{7-3\sqrt5}{4},\,±\frac{3-\sqrt5}{4},\,±1,\,±\frac{6+\sqrt5}{2}\right),$$
 * $$\left(±\frac{7-3\sqrt5}{4},\,±\frac{\sqrt5-1}{2},\,±\frac{4+\sqrt5}{2},\,±\frac{9+\sqrt55}{4}\right),$$
 * $$\left(±\frac{7-3\sqrt5}{4},\,±\frac{7-\sqrt5}{4},\,±\frac{1+\sqrt5}{2},\,±\frac{3+2\sqrt5}{2}\right),$$
 * $$\left(±\frac{7-3\sqrt5}{4},\,±\frac{3+\sqrt5}{4},\,±\frac{1+3\sqrt5}{4},\,±\frac{3+5\sqrt5}{4}\right),$$
 * $$\left(±\frac{\sqrt5-2}{2},\,±\frac{3\sqrt5-5}{4},\,±\frac{11+\sqrt5}{4},\,±\frac{3+\sqrt5}{2}\right),$$
 * $$\left(±\frac{\sqrt5-2}{2},\,±\frac12,\,±\frac{4-\sqrt5}{2},\,±\frac{6+\sqrt5}{2}\right),$$
 * $$\left(±\frac{\sqrt5-2}{2},\,±\frac{7-\sqrt5}{4},\,±\frac{3+\sqrt5}{4},\,±\frac{1+3\sqrt5}{2}\right),$$
 * $$\left(±\frac{\sqrt5-2}{2},\,±(\sqrt5-1),\,±\frac{9+\sqrt5}{4},\,±\frac{5+3\sqrt5}{4}\right),$$
 * $$\left(±\frac{\sqrt5-2}{2},\,±\frac32,\,±\frac{2+\sqrt5}{2},\,±\frac{3\sqrt5}{2}\right),$$
 * $$\left(±\frac{3-\sqrt5}{4},\,±\frac{3-\sqrt5}{2},\,±3\frac{\sqrt5-1}{4},\,±\frac{6+\sqrt5}{2}\right),$$
 * $$\left(±\frac{3-\sqrt5}{4},\,±\frac{3\sqrt5-5}{4},\,±\frac{13+\sqrt5}{4},\,±\frac{5+\sqrt5}{4}\right),$$
 * $$\left(±\frac{3-\sqrt5}{4},\,±\frac12,\,±\frac{1+3\sqrt5}{2},\,±\frac{9-\sqrt5}{4}\right),$$
 * $$\left(±\frac{3-\sqrt5}{4},\,±\frac12,\,±(1+\sqrt5),\,±\frac{13-\sqrt5}{4}\right),$$
 * $$\left(±\frac{3-\sqrt5}{4},\,±\frac{\sqrt5}{2},\,±\frac{3\sqrt5-1}{2},\,±\frac{5+3\sqrt5}{4}\right),$$
 * $$\left(±\frac{3-\sqrt5}{4},\,±\frac{7-\sqrt5}{4},\,±\frac{3\sqrt5-1}{4},\,±\frac{13+\sqrt5}{4}\right),$$
 * $$\left(±\frac{3-\sqrt5}{4},\,±\frac{3\sqrt5-1}{4},\,±\frac{5\sqrt5-3}{4},\,±\frac{7+3\sqrt5}{4}\right),$$
 * $$\left(±\frac{3-\sqrt5}{4},\,±\frac{5\sqrt5-3}{4},\,±\frac{9+\sqrt5}{4},\,±3\frac{1+\sqrt5}{4}\right),$$
 * $$\left(±\frac{3-\sqrt5}{4},\,±\frac{2+\sqrt5}{2},\,±\frac{3\sqrt5-1}{2},\,±\frac{7+\sqrt5}{4}\right),$$
 * $$\left(±\frac{3-\sqrt5}{2},\,±\frac{3\sqrt5-5}{4},\,±\frac{3+2\sqrt5}{2},\,±\frac{9-\sqrt5}{4}\right),$$
 * $$\left(±\frac{3-\sqrt5}{2},\,±\frac{\sqrt5-1}{2},\,±\frac{1+3\sqrt5}{2},\,±\frac{1+\sqrt5}{2}\right),$$
 * $$\left(±\frac{3-\sqrt5}{2},\,±\frac{2+\sqrt5}{2},\,±\frac{5+3\sqrt5}{4},\,±\frac{11-\sqrt5}{4}\right),$$
 * $$\left(±\frac{3-\sqrt5}{2},\,±\frac{1+3\sqrt5}{4},\,±\frac{9+\sqrt5}{4},\,±\frac52\right),$$
 * $$\left(±\frac{3\sqrt5-5}{4},\,±\frac12,\,±\sqrt5,\,±\frac{3+5\sqrt5}{4}\right),$$
 * $$\left(±\frac{3-\sqrt5-5}{4},\,±\frac{\sqrt5-1}{2},\,±\frac{5-\sqrt5}{4},\,±\frac{6+\sqrt5}{2}\right),$$
 * $$\left(±\frac{3\sqrt5-5}{4},\,±\frac{\sqrt5}{2},\,±\frac{1+3\sqrt5}{2},\,±\frac{3+\sqrt5}{4}\right),$$
 * $$\left(±\frac{3\sqrt5-5}{4},\,±\frac{9-\sqrt5}{4},\,±\frac{2+\sqrt5}{2},\,±(1+\sqrt5)\right),$$
 * $$\left(±\frac12,\,±\frac{\sqrt5-1}{2},\,±\frac{11-\sqrt5}{4},\,±\frac{3+5\sqrt5}{4}\right),$$
 * $$\left(±\frac12,\,±\frac{\sqrt5-1}{2},\,±\frac{13+\sqrt5}{4},\,±\frac{9-\sqrt5}{4}\right),$$
 * $$\left(±\frac12,\,±3\frac{\sqrt5-1}{4},\,±\frac{1+3\sqrt5}{2},\,±\frac{3\sqrt5-1}{4}\right),$$
 * $$\left(±\frac12,\,±(\sqrt5-1),\,±\frac{13+\sqrt5}{4},\,±\frac{3+\sqrt5}{4}\right),$$
 * $$\left(±\frac12,\,±\frac{3+\sqrt5}{4},\,±\frac{1+3\sqrt5}{2},\,±\frac{9+\sqrt5}{4}\right),$$
 * $$\left(±\frac12,\,±\frac{1+\sqrt5}{2},\,±\frac{5\sqrt5-3}{4},\,±\frac{11+\sqrt5}{4}\right),$$
 * $$\left(±\frac12,\,±\frac{1+\sqrt5}{2},\,±\frac{9+\sqrt5}{4},\,±\frac{13-\sqrt5}{4}\right),$$
 * $$\left(±\frac12,\,±\frac{6-\sqrt5}{2},\,±\frac{2+\sqrt5}{2},\,±\frac{4+\sqrt5}{2}\right),$$
 * $$\left(±\frac12,\,±\frac{1+3\sqrt5}{4},\,±\frac{3\sqrt5-1}{2},\,±3\frac{1+\sqrt5}{4}\right),$$
 * $$\left(±\frac12,\,±\frac{5\sqrt5-3}{4},\,±\frac{5+3\sqrt5}{4},\,±\sqrt5\right),$$
 * $$\left(±\frac{\sqrt5-1}{2},\,±\frac{5-\sqrt5}{4},\,±3\frac{1+\sqrt5}{4},\,±\frac{3\sqrt5}{2}\right),$$
 * $$\left(±\frac{\sqrt5-1}{2},\,±\frac{2\sqrt5-3}{2},\,±\frac{7+\sqrt5}{4},\,±\frac{7+3\sqrt5}{4}\right),$$
 * $$\left(±\frac{\sqrt5-1}{2},\,±3\frac{\sqrt5-1}{4},\,±\frac{13+\sqrt5}{4},\,±\frac32\right),$$
 * $$\left(±\frac{\sqrt5-1}{2},\,±\frac{1+\sqrt5}{2},\,±\frac{3\sqrt5-1}{2},\,±\frac{3+\sqrt5}{2}\right),$$
 * $$\left(±\frac{\sqrt5-1}{2},\,±\frac{1+3\sqrt5}{4},\,±\frac{5\sqrt5-1}{4},\,±\frac{4+\sqrt5}{2}\right),$$
 * $$\left(±\frac{5-\sqrt5}{4},\,±(\sqrt5-1),\,±\frac{3+2\sqrt5}{2},\,±\frac{3\sqrt5-1}{4}\right),$$
 * $$\left(±\frac{5-\sqrt5}{4},\,±\frac{3+\sqrt5}{4},\,±\frac{5+3\sqrt5}{4},\,±\frac{13-\sqrt5}{4}\right),$$
 * $$\left(±\frac{5-\sqrt5}{4},\,±\frac{9-\sqrt5}{4},\,±\frac{1+3\sqrt5}{4},\,±\frac{11+\sqrt5}{4}\right),$$
 * $$\left(±\frac{2\sqrt5-3}{2},\,±\frac{\sqrt5}{2},\,±\frac{3+2\sqrt5}{2},\,±\frac32\right),$$
 * $$\left(±\frac{2\sqrt5-3}{2},\,±\frac{3\sqrt5-1}{4},\,±\frac{5+3\sqrt5}{4},\,±\frac{3+\sqrt5}{2}\right),$$
 * $$\left(±\frac{2\sqrt5-3}{2},\,±\frac{5+\sqrt5}{4},\,±\frac{1+3\sqrt5}{4},\,±(1+\sqrt5)\right),$$
 * $$\left(±\frac{4-\sqrt5}{2},\,±3\frac{\sqrt5-1}{4},\,±(1+\sqrt5),\,±3\frac{1+\sqrt5}{4}\right),$$
 * $$\left(±\frac{4-\sqrt5}{2},\,±\frac{\sqrt5}{2},\,±\frac{4+\sqrt5}{2},\,±\frac52\right),$$
 * $$\left(±\frac{4-\sqrt5}{2},\,±\frac{3\sqrt5-1}{4},\,±\frac{3+5\sqrt5}{4},\,±\frac{1+\sqrt5}{2}\right),$$
 * $$\left(±\frac{4-\sqrt5}{2},\,±\frac{1+\sqrt5}{2},\,±\frac{7+3\sqrt5}{4},\,±\frac{9-\sqrt5}{4}\right),$$
 * $$\left(±3\frac{\sqrt5-1}{4},\,±(\sqrt5-1),\,±\frac{4+\sqrt5}{2},\,±3\frac{1+\sqrt5}{4}\right),$$
 * $$\left(±3\frac{\sqrt5-1}{4},\,±\frac{3+\sqrt5}{4},\,±\frac{3+5\sqrt5}{4},\,±\frac{9-\sqrt5}{4}\right),$$
 * $$\left(±3\frac{\sqrt5-1}{4},\,±\frac{1+\sqrt5}{2},\,±\frac{3\sqrt5}{2},\,±\frac{5+\sqrt5}{4}\right),$$
 * $$\left(±1,\,±\frac{\sqrt5}{2},\,±\frac{11+\sqrt5}{4},\,±\frac{11-\sqrt5}{4}\right),$$
 * $$\left(±1,\,±(\sqrt5-1),\,±(1+\sqrt5),\,±\sqrt5\right),$$
 * $$\left(±1,\,±\frac{3+\sqrt5}{4},\,±\frac{7+3\sqrt5}{4},\,±\frac{6-\sqrt5}{2}\right),$$
 * $$\left(±1,\,±\frac{3\sqrt5-1}{4},\,±\frac{3\sqrt5}{2},\,±\frac{1+3\sqrt5}{4}\right),$$
 * $$\left(±\frac{3+\sqrt5}{4},\,±\frac{6-\sqrt5}{2},\,±3\frac{1+\sqrt5}{4},\,±\frac{3+\sqrt5}{2}\right),$$
 * $$\left(±\frac{7-\sqrt5}{4},\,±\sqrt5,\,±\frac{9+\sqrt5}{4},\,±\frac52\right),$$
 * $$\left(±\frac{3+\sqrt5}{4},\,±\frac{1+3\sqrt5}{4},\,±\frac{7+\sqrt5}{4},\,±\frac{13-\sqrt5}{4}\right),$$
 * $$\left(±\frac{3\sqrt5-1}{4},\,±\frac{9-\sqrt5}{4},\,±\frac52,\,±\frac{3+\sqrt5}{2}\right),$$
 * $$\left(±\frac{3\sqrt5-1}{4},\,±\frac{5+\sqrt5}{4},\,±\frac{11-\sqrt5}{4},\,±\frac{9+\sqrt5}{4}\right),$$
 * $$\left(±\frac32,\,±\frac{1+\sqrt5}{2},\,±3\frac{1+\sqrt5}{4},\,±\frac{13-\sqrt5}{4}\right),$$
 * $$\left(±\frac32,\,±\frac{9-\sqrt5}{4},\,±\sqrt5,\,±\frac{9+\sqrt5}{4}\right),$$
 * $$\left(±\frac{1+\sqrt5}{2},\,±\frac{5+\sqrt5}{4},\,±\frac{6-\sqrt5}{2},\,±\frac{5+3\sqrt5}{4}\right).$$