Quasiprismatorhombated grand hecatonicosachoron

The quasiprismatorhombated grand hecatonicosachoron, or quippirghi, is a nonconvex uniform polychoron that consists of 720 pentagonal prisms, 720 decagrammic prisms, 120 quasitruncated great stellated dodecahedra, and 120 small rhombicosidodecahedra. 1 pentagonal prism, 2 decagrammic prisms, 1 small rhombicosidodecahedron, and 1 quasitruncated great stellated dodecahedron join at each vertex. It can be obtained by quasiruncitruncating the great stellated hecatonicosachoron.

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

Related polychora
The quasiprismatorhombated grand hecatonicosachoron is the colonel of a three-member ergiment that also includes the grand prismatotrishecatonicosachoron and the rhombiprismic hecatonicosihecatonicosachoron.