Small rhombated grand stellated hecatonicosachoron

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

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

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