Small rhombated grand hexacosichoron

The small rhombated grand hexacosichoron, or sirgax, is a nonconvex uniform polychoron that consists of 600 cuboctahedra, 720 pentagrammic prisms, and 120 great icosidodecahedra. 1 great icosidodecahedron, 2 pentagrammic prisms, and 2 cuboctahedra join at each vertex. It can be obtained by cantellating the grand hexacosichoron.

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

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