Small rhombated hexacosichoron

The small rhombated hexacosichoron, or srix, also commonly called the cantellated 600-cell, is a convex uniform polychoron that consists of 600 cuboctahedra, 720 pentagonal prisms, and 120 icosidodecahedra. 1 icosidodecahedron, 2 pentagonal prisms, and 2 cuboctahedra join at each vertex. As one of its names suggests, it can be obtained by cantellating the hexacosichoron.

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

Semi-uniform variant
The small rhombated hexacosichoron has a semi-uniform variant of the form o5y3o3x that maintains its full symmetry. This variant uses 120 icosidodecahedra of size y, 600 rhombitetratetrahedra of form x3o3y, and 720 pentagonal prisms of form x y5o as cells, with 2 edge lengths.

With edges of length a (surrounds 2 rhombitetratetrahedra) and b (of icosidodecahedra), its circumradius is given by $$\sqrt{\frac{3a^2+21b^2+14ab+(a^2+9b^2+6ab)\sqrt5}{2}}$$.

Related polychora
The small rhombated hexacosichoron is the colonel of a seven-member regiment. Its other members include the small retrosphenoverted hecatonicosihexacosihecatonicosachoron, rhombic small hexacosihecatonicosachoron, pseudorhombic small dishecatonicosachoron, grand rhombic small hexacosihecatonicosachoron, small dishecatonicosintercepted hexacosihecatonicosachoron, and hecatonicosintercepted prismatohexacosihecatonicosachoron.

The segmentochoron icosidodecahedron atop truncated icosahedron can be obtained as a cap of the small rhombated hexacosichoron.