Small rhombated hecatonicosachoron

The small rhombated hecatonicoscahoron, or srahi, also commonly called the cantellated 120-cell, is a convex uniform polychoron that consists of 600 regular octahedra, 1200 triangular prisms, and 120 small rhombicosidodecahedra. 1 octahedron, 2 triangular prisms, and 2 small rhombicosidodecahedra join at each vertex. As one of its names suggests, it can be obtained by cantellating the hecatonicosachoron.

Vertex coordinates
Coordinates for the vertices of a small rhombated hecatonicosachoron of edge length 1 are given by all permutations of: together with all even permutations of:
 * $$\left(0,\,0,\,±(2+\sqrt5),\,±(3+\sqrt5)\right),$$
 * $$\left(±\frac12,\,±\frac12,\,±\frac{2+\sqrt5}{2},\,±3\frac{2+\sqrt5}{2}\right),$$
 * $$\left(±\frac12,\,±\frac12,\,±\frac{5+2\sqrt5}{2},\,±\frac{5+2\sqrt5}{2}\right),$$
 * $$\left(±\frac{1+\sqrt5}{2},\,±\frac{3+\sqrt5}{2},\,±(2+\sqrt5),\,±(2+\sqrt5)\right),$$
 * $$\left(±\frac{2+\sqrt5}{2},\,±\frac{2+\sqrt5}{2},\,±\frac{3+2\sqrt5}{2},\,±\frac{5+2\sqrt5}{2}\right),$$
 * $$\left(0,\,±\frac12,\,±\frac{13+5\sqrt5}{4},\,±\frac{5+3\sqrt5}{4}\right),$$
 * $$\left(0,\,±\frac{1+\sqrt5}{4},\,±\frac{11+5\sqrt5}{4},\,±\frac{3+2\sqrt5}{2}\right),$$
 * $$\left(0,\,±\frac{3+\sqrt5}{4},\,±3\frac{2+\sqrt5}{2},\,±\frac{5+\sqrt5}{4}\right),$$
 * $$\left(0,\,±\frac{2+\sqrt5}{2},\,±\frac{9+5\sqrt5}{4},\,±3\frac{3+\sqrt5}{4}\right),$$
 * $$\left(±\frac12,\,±\frac{3+\sqrt5}{4},\,±\frac{9+5\sqrt5}{4},\,±(2+\sqrt5)\right),$$
 * $$\left(±\frac12,\,±\frac{3+\sqrt5}{4},\,±\frac{13+5\sqrt5}{4},\,±\frac{3+\sqrt5}{2}\right),$$
 * $$\left(±\frac12,\,±\frac{1+\sqrt5}{2},\,±\frac{11+5\sqrt5}{4},\,±\frac{7+3\sqrt5}{4}\right),$$
 * $$\left(±\frac12,\,±\frac{7+3\sqrt5}{4},\,±(2+\sqrt5),\,±3\frac{3+\sqrt5}{4}\right),$$
 * $$\left(±\frac{1+\sqrt5}{4},\,±\frac{3+\sqrt5}{4},\,±\frac{1+\sqrt5}{2},\,±3\frac{2+\sqrt5}{2}\right),$$
 * $$\left(±\frac{1+\sqrt5}{4},\,±\frac{3+\sqrt5}{2},\,±\frac{5+2\sqrt5}{2},\,±3\frac{3+\sqrt5}{4}\right),$$
 * $$\left(±\frac{3+\sqrt5}{4},\,±\frac{1+\sqrt5}{2},\,±\frac{13+5\sqrt5}{4},\,±\frac{2+\sqrt5}{2}\right),$$
 * $$\left(±\frac{3+\sqrt5}{4},\,±\frac{5+\sqrt5}{4},\,±\frac{5+2\sqrt5}{2},\,±(2+\sqrt5)\right),$$
 * $$\left(±\frac{3+\sqrt5}{4},\,±\frac{2+\sqrt5}{2},\,±(3+\sqrt5),\,±\frac{7+3\sqrt5}{4}\right),$$
 * $$\left(±\frac{3+\sqrt5}{4},\,±\frac{7+3\sqrt5}{4},\,±\frac{3+2\sqrt5}{2},\,±(2+\sqrt5)\right),$$
 * $$\left(±\frac{1+\sqrt5}{2},\,±\frac{5+3\sqrt5}{4},\,±\frac{5+2\sqrt5}{2},\,±\frac{7+3\sqrt5}{4}\right),$$
 * $$\left(±\frac{5+\sqrt5}{4},\,±\frac{2+\sqrt5}{2},\,±\frac{11+5\sqrt5}{4},\,±\frac{3+\sqrt5}{2}\right),$$
 * $$\left(±\frac{2+\sqrt5}{2},\,±\frac{3+\sqrt5}{2},\,±\frac{5+3\sqrt5}{4},\,±\frac{9+5\sqrt5}{4}\right).$$

Semi-uniform variant
The small rhombated hecatonicosachoron has a semi-uniform variant of the form x5o3y3o that maintains its full symmetry. This variant uses 600 octahedra of size y, 120 semi-uniform small rhombicosidodecahedra of form x5o3y, and 1200 triangular prisms of form x y3o as cells, with 2 edge lengths.

With edges of length a (surrounded by two small rhombicosidodecahedra) and b (of octahedra), its circumradius is given by $$\sqrt{7a^2+5b^2+11ab+(3a^2+2b^2+5ab)\sqrt5}$$.

Related polychora
The small rhombated hecatonicosachoron is the colonel of a seven-member regiment. Its other members include the small retrosphenoverted hexacosidishecatonicosachoron, small rhombic dishecatonicosachoron, small pseudorhombic dishecatonicosachoron, grand rhombic prismatohecatonicosachoron, prismatohecatonicosintercepted hexacosihecatonicosachoron, and prismatointercepted prismatohexacosihecatonicosachoron.

The segmentochoron small rhombicosidodecahedron atop truncated dodecahedron can be obtained as a cap of the small rhombated hecatonicosachoron. Another possible cap is the pentagonal pucofastegium.