Small rhombated small stellated hecatonicosachoron

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

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

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