Small rhombated grand hecatonicosachoron

The small rhombated grand hecatonicosachoron, or sraghi, is a nonconvex uniform polychoron that consists of 720 pentagrammic prisms, 120 great icosidodecahedra, and 120 small rhombicosidodecahedra. 1 great icosidodecahedron, 2 pentagrammic prisms, and 2 small rhombicosidodecahedra join at each vertex. It can be obtained by cantellating the grand hecatonicosachoron.

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

=Related polychora==

The small rhombated grand hecatonicosachoron is the colonel of a regiment of 7 members. Its other members include the retrosphenoverted trishecatonicosachoron, small rhombic hecatonicosihecatonicosachoron, pseudorhombic dishecatonicosachoron, grand rhombic hecatonicosihecatonicosachoron, dishecatonicosintercepted dishecatonicosachoron, and hecatonicosintercepted hecatonicosiprismatohecatonicosachoron.