Prismatorhombated great grand hecatonicosachoron

The prismatorhombated great grand hecatonicosachoron, or pirgaghi, is a nonconvex uniform polychoron that consists of 720 pentagonal prisms, 1200 hexagonal prisms, 120 truncated great icosahedra, and 120 rhombidodecadodecahedra. 1 pentagonal prism, 2 hexagonal prisms, 1 truncated great icosahedron, and 1 rhombidodecadodecahedron join at each vertex. It can be obtained by runcitruncating the great faceted hexacosichoron.

Vertex coordinates
The vertices of a prismatorhombated great grand hecatonicosachoron of edge length 1 are given by all permutations of: plus all even permutations of:
 * $$\left(±\frac12,\,±\frac12,\,±\frac{\sqrt5}{2},\,±\frac{3\sqrt5-4}{2}\right),$$
 * $$\left(±\frac12,\,±\frac12,\,±\frac{2\sqrt5-1}{2},\,±\frac{5-2\sqrt5}{2}\right),$$
 * $$\left(±1,\,±1,\,±(\sqrt5-1),\,±(\sqrt5-2)\right),$$
 * $$\left(±\frac{\sqrt5-2}{2},\,±\frac{\sqrt5-2}{2},\,±\frac{2\sqrt5-1}{2},\,±\frac{2\sqrt5-3}{2}\right),$$
 * $$\left(±(\sqrt5-1),\,±(\sqrt5-1),\,±\frac{\sqrt5-1}{2},\,±\frac{3-\sqrt5}{2}\right),$$
 * $$\left(±\frac{2\sqrt5-3}{2},\,±\frac{2\sqrt5-3}{2},\,±\frac12,\,±\frac32\right),$$
 * $$\left(0,\,±\frac{3+\sqrt5}{4},\,±\frac{3\sqrt5-4}{2},\,±\frac{3-\sqrt5}{4}\right),$$
 * $$\left(0,\,±\frac12,\,±\frac{13-3\sqrt5}{4},\,±3\frac{\sqrt5-1}{4}\right),$$
 * $$\left(0,\,±\frac{5+\sqrt5}{4},\,±\frac{5\sqrt5-9}{4},\,±\frac{\sqrt5-2}{2}\right),$$
 * $$\left(0,\,±\frac{3-\sqrt5}{2},\,±\frac{5-\sqrt5}{2},\,±(\sqrt5-1)\right),$$
 * $$\left(0,\,±\frac{9-\sqrt5}{4},\,±\frac{2\sqrt5-1}{2},\,±\frac{3\sqrt5-5}{4}\right),$$
 * $$\left(±\frac{3+\sqrt5}{4},\,±1,\,±3\frac{3-\sqrt5}{4},\,±\frac{2\sqrt5-3}{2}\right),$$
 * $$\left(±\frac{3+\sqrt5}{4},\,±\frac{\sqrt5-1}{2},\,±\frac{7-\sqrt5}{4},\,±\frac{5-2\sqrt5}{2}\right),$$
 * $$\left(±\frac{1+\sqrt5}{4},\,±\frac12,\,±\frac{11-3\sqrt5}{4},\,±(\sqrt5-1)\right),$$
 * $$\left(±\frac{1+\sqrt5}{4},\,±\frac{\sqrt5-1}{4},\,±1,\,±\frac{3\sqrt5-4}{2}\right),$$
 * $$\left(±\frac{1+\sqrt5}{4},\,±\frac32,\,±\frac{5\sqrt5-9}{4},\,±\frac{\sqrt5-1}{2}\right),$$
 * $$\left(±\frac{1+\sqrt5}{4},\,±\frac{5-\sqrt5}{4},\,±\frac{5-\sqrt5}{2},\,±\frac{2\sqrt5-3}{2}\right),$$
 * $$\left(±\frac{1+\sqrt5}{4},\,±\frac{\sqrt5-2}{2},\,±\frac{9-\sqrt5}{4},\,±(\sqrt5-2)\right),$$
 * $$\left(±\frac12,\,±\frac{5+\sqrt5}{4},\,±(\sqrt5-2),\,±\frac{7-3\sqrt5}{4}\right),$$
 * $$\left(±\frac12,\,±1,\,±\frac{5\sqrt5-9}{4},\,±\frac{3\sqrt5-1}{4}\right),$$
 * $$\left(±\frac12,\,±\frac{\sqrt5-1}{2},\,±\frac{5-\sqrt5}{4},\,±\frac{13-3\sqrt5}{4}\right),$$
 * $$\left(±\frac12,\,±\frac{3\sqrt5-1}{4},\,±\frac{3-\sqrt5}{2},\,±\frac{11-3\sqrt5}{4}\right),$$
 * $$\left(±\frac12,\,±\frac{7-\sqrt5}{4},\,±\frac{5-\sqrt5}{2},\,±\frac{7-3\sqrt5}{4}\right),$$
 * $$\left(±\frac12,\,±\frac{3-\sqrt5}{2},\,±\frac{9-\sqrt5}{4},\,±3\frac{3-\sqrt5}{4}\right),$$
 * $$\left(±\frac{5+\sqrt5}{4},\,±\frac{\sqrt5-1}{4},\,±\frac{3-\sqrt5}{2},\,±\frac{5-2\sqrt5}{2}\right),$$
 * $$\left(±\frac{\sqrt5-1}{4},\,±1,\,±\frac{13-3\sqrt5}{4},\,±\frac{\sqrt5-2}{2}\right),$$
 * $$\left(±\frac{\sqrt5-1}{4},\,±\frac{7-\sqrt5}{4},\,±\frac{2\sqrt5-3}{2},\,±(\sqrt5-1)\right),$$
 * $$\left(±\frac{\sqrt5-1}{4},\,±\frac{3-\sqrt5}{2},\,±3\frac{3-\sqrt5}{4},\,±\frac{2\sqrt5-1}{2}\right),$$
 * $$\left(±1,\,±\frac{\sqrt5}{2},\,±\frac{3\sqrt5-5}{4},\,±\frac{11-3\sqrt5}{4}\right),$$
 * $$\left(±1,\,±\frac32,\,±3\frac{3-\sqrt5}{4},\,±\frac{7-3\sqrt5}{4}\right),$$
 * $$\left(±1,\,±\frac{5-\sqrt5}{4},\,±\frac{5-2\sqrt5}{2},\,±\frac{3\sqrt5-1}{4}\right),$$
 * $$\left(±1,\,±\frac{\sqrt5-2}{2},\,±\frac{7-\sqrt5}{4},\,±\frac{11-3\sqrt5}{4}\right),$$
 * $$\left(±\frac{\sqrt5}{2},\,±\frac32,\,±\frac{5-2\sqrt5}{2},\,±\frac{\sqrt5-2}{2}\right),$$
 * $$\left(±\frac{\sqrt5}{2},\,±\frac{5-\sqrt5}{4},\,±3\frac{3-\sqrt5}{4},\,±(\sqrt5-1)\right),$$
 * $$\left(±\frac{\sqrt5}{2},\,±\frac{7-\sqrt5}{4},\,±(\sqrt5-2),\,±3\frac{\sqrt5-1}{4}\right),$$
 * $$\left(±\frac{3-\sqrt5}{4},\,±\frac32,\,±\frac{11-3\sqrt5}{4},\,±\frac{3-\sqrt5}{2}\right),$$
 * $$\left(±\frac{3-\sqrt5}{4},\,±\frac{5-\sqrt5}{4},\,±(\sqrt5-2),\,±\frac{2\sqrt5-1}{2}\right),$$
 * $$\left(±\frac{\sqrt5-1}{2},\,±\frac{2\sqrt5-1}{2},\,±\frac{3\sqrt5-5}{4},\,±\frac{7-3\sqrt5}{4}\right),$$
 * $$\left(±\frac{3\sqrt5-1}{4},\,±\frac{\sqrt5-2}{2},\,±\frac{7-3\sqrt5}{4},\,±(\sqrt5-1)\right),$$
 * $$\left(±\frac{3\sqrt5-1}{4},\,±3\frac{\sqrt5-1}{4},\,±\frac{3-\sqrt5}{2},\,±\frac{2\sqrt5-1}{2}\right).$$

Related polychora
The prismatorhombated great grand hecatonicosachoron is the colonel of a 3-member regiment that also includes the great prismatohecatonicosihecatonicosihexacosichoron and the great rhombiprismic hecatonicosihexacosichoron.