Prismatorhombated stellated hecatonicosachoron

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

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

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