Small rhombated great grand hecatonicosachoron

The small rhombated great grand hecatonicosachoron, or sirgaghi, is a nonconvex uniform polychoron that consists of 1200 triangular prisms, 120 great icosidodecahedra, and 120 rhombidodecadodecahedra. 1 great icosidodecahedron, 2 triangular prisms, and 2 rhombidodecadodecahedra join at each vertex. it can be obtained by cantellating the great grand hecatonicosachoron.

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

Related polychora
The small rhombated great grand hecatonicosachoron is the colonel of a regiment of 7 members. Its other members include the great retrosphenoverted hecatonicosihexacosihecatonicosachoron, rhombic great hecatonicosihexacosichoron, pseudorhombic great hexacosihecatonicosachoron, grand rhombic great dishecatonicosachoron, great hexacosihecatonicosintercepted dishecatonicosachoron, and great hecatonicosintercepted prismatodishecatonicosachoron.