Small rhombated great hecatonicosachoron

The small rhombated great hecatonicosachoron, or sirghi, is a nonconvex uniform polychoron that consists of 720 pentagonal prisms, 120 dodecadodecahedra, and 120 rhombidodecadodecahedra. 1 dodecadodecahedron, 2 pentagonal prisms, and 2 rhombidodecadodecahedra join at each vertex. it can be obtained by cantellating the great hecatonicosachoron.

Vertex coordinates
Coordinates for the vertices of a small rhombated great hecatonicosachoron of edge length 1 are given by all permutations of: together with all even permutations of:
 * $$\left(0,\,0,\,±1,\,±(1+\sqrt5)\right),$$
 * $$\left(±\frac{2+\sqrt5}{2},\,±\frac{2+\sqrt5}{2},\,±\frac12,\,±\frac32\right),$$
 * $$\left(±\frac{2+\sqrt5}{2},\,±\frac{2+\sqrt5}{2},\,±\frac{\sqrt5}{2},\,±\frac{\sqrt5}{2}\right),$$
 * $$\left(±\frac{3+\sqrt5}{2},\,±\frac{1+\sqrt5}{2},\,±1,\,±1\right),$$
 * $$\left(±\frac12,\,±\frac12,\,±\frac{4+\sqrt5}{2},\,±\frac{\sqrt5}{2}\right),$$
 * $$\left(0,\,±\frac{2+\sqrt5}{2},\,±\frac{1+3\sqrt5}{4},\,±\frac{5+\sqrt5}{4}\right),$$
 * $$\left(0,\,±\frac{3+\sqrt5}{4},\,±\frac{3+\sqrt5}{4},\,±\frac{4+\sqrt5}{2}\right),$$
 * $$\left(0,\,±\frac{1+\sqrt5}{4},\,±\frac32,\,±\frac{5+3\sqrt5}{4}\right),$$
 * $$\left(0,\,±\frac12,\,±\frac{7+\sqrt5}{4},\,±3\frac{1+\sqrt5}{4}\right),$$
 * $$\left(±\frac{2+\sqrt5}{2},\,±\frac{1+\sqrt5}{4},\,±\frac{7+\sqrt5}{4},\,±1\right),$$
 * $$\left(±\frac{2+\sqrt5}{2},\,±\frac{1+\sqrt5}{4},\,±\frac{1+3\sqrt5}{4},\,±\frac{1+\sqrt5}{2}\right),$$
 * $$\left(±\frac{2+\sqrt5}{2},\,±\frac{3+\sqrt5}{2},\,±\frac{3-\sqrt5}{4},\,±\frac{\sqrt5-1}{4}\right),$$
 * $$\left(±\frac{2+\sqrt5}{2},\,±\frac{\sqrt5-1}{4},\,±1,\,±3\frac{1+\sqrt5}{4}\right),$$
 * $$\left(±\frac{3+\sqrt5}{4},\,±\frac{1+\sqrt5}{4},\,±\frac{3+\sqrt5}{2},\,±\frac32\right),$$
 * $$\left(±\frac{3+\sqrt5}{4},\,±\frac{1+\sqrt5}{2},\,±\frac{\sqrt5}{2},\,±3\frac{1+\sqrt5}{4}\right),$$
 * $$\left(±\frac{1+\sqrt5}{4},\,±\frac{3+\sqrt5}{2},\,±\frac{1+3\sqrt5}{4},\,±\frac12\right),$$
 * $$\left(±\frac{1+\sqrt5}{4},\,±\frac{5+3\sqrt5}{4},\,±\frac{\sqrt5}{2},\,±1\right),$$
 * $$\left(±\frac{1+\sqrt5}{4},\,±\frac12,\,±(1+\sqrt5),\,±\frac{\sqrt5-1}{4}\right),$$
 * $$\left(±\frac{1+\sqrt5}{4},\,±\frac{\sqrt5-1}{4},\,±\frac{4+\sqrt5}{2},\,±1\right),$$
 * $$\left(±\frac{3+\sqrt5}{2},\,±\frac{5+\sqrt5}{4},\,±\frac{\sqrt5}{2},\,±\frac{\sqrt5-1}{4}\right),$$
 * $$\left(±\frac{5+3\sqrt5}{4},\,±\frac12,\,±\frac{3-\sqrt5}{4},\,±\frac{1+\sqrt5}{2}\right),$$
 * $$\left(±\frac12,\,±\frac{1+\sqrt5}{2},\,±\frac{5+\sqrt5}{4},\,±\frac{7+\sqrt5}{4}\right).$$

Related polychora
The small rhombated great hecatonicosachoron is the colonel of a regiment with 7 members. Its other members include the small retrosphenoverted hecatonicosidishecatonicosachoron, rhombic small dishecatonicosachoron, pseudorhombic small hecatonicosihexacosichoron, grand rhombic small hecatonicosihexacosichoron, small hecatonicosihexacosintercepted dishecatonicosachoron, and small hexacosintercepted prismatodishecatonicosachoron.