Great skewverted hexacositrishecatonicosachoron

The great skewverted hexacositrishecatonicosachoron, or gik vixathi, is a nonconvex uniform polychoron that consists of 600 cuboctahedra, 120 small icosicosidodecahedra, 120 great dodecicosidodecahedra, and 120 great quasitruncated icosidodecahedra. 1 cuboctahedron, 1 small icosicosidodecahedron, 1 great dodecicosidodecahedron, and 2 great quasitruncated icosidodecahedra join at each vertex.

Vertex coordinates
The vertices of a great skewverted hexacositrishecatonicosachoron of edge length 1 are given by all permutations of: Plus all even permutations of:
 * $$\left(0,\,±1,\,±(\sqrt5-1),\,±(\sqrt5-1)\right),$$
 * $$\left(±\frac12,\,±\frac12,\,±\frac{\sqrt5-2}{2},\,±\frac{6-\sqrt5}{2}\right),$$
 * $$\left(±\frac12,\,±\frac12,\,±\frac{2\sqrt5-1}{2},\,±\frac{2\sqrt5-3}{2}\right),$$
 * $$\left(±1,\,±1,\,±\frac{3-\sqrt5}{2},\,±\frac{5-\sqrt5}{2}\right),$$
 * $$\left(±\frac{4-\sqrt5}{2},\,±\frac{4-\sqrt5}{2},\,±\frac12,\,±\frac32\right),$$
 * $$\left(0,\,±\frac{3+\sqrt5}{4},\,±\frac{\sqrt5}{2},\,±\frac{5\sqrt5-7}{4}\right),$$
 * $$\left(0,\,±\frac{5+\sqrt5}{4},\,±\frac{7-3\sqrt5}{4},\,±\frac{4-\sqrt5}{2}\right),$$
 * $$\left(0,\,±\frac{3-\sqrt5}{4},\,±\frac{5-\sqrt5}{4},\,±\frac{6-\sqrt5}{2}\right),$$
 * $$\left(0,\,±\frac{1+3\sqrt5}{4},\,±\frac{\sqrt5-2}{2},\,±3\frac{3-\sqrt5}{4}\right),$$
 * $$\left(±\frac{3+\sqrt5}{4},\,±\frac12,\,±1,\,±\frac{5\sqrt5-7}{4}\right),$$
 * $$\left(±\frac{3+\sqrt5}{4},\,±\frac12,\,±\frac{5-\sqrt5}{2},\,±\frac{3\sqrt5-5}{4}\right),$$
 * $$\left(±\frac{3+\sqrt5}{4},\,±\frac12,\,±(\sqrt5-2),\,±\frac{3\sqrt5-1}{4}\right),$$
 * $$\left(±\frac{3+\sqrt5}{4},\,±\frac{3-\sqrt5}{4},\,±\frac32,\,±(\sqrt5-2)\right),$$
 * $$\left(±\frac{3+\sqrt5}{4},\,±\frac{3-\sqrt5}{4},\,±\frac{4-\sqrt5}{2},\,±(\sqrt5-1)\right),$$
 * $$\left(±\frac{3+\sqrt5}{4},\,±\frac{\sqrt5-1}{2},\,±\frac{7-\sqrt5}{4},\,±\frac{2\sqrt5-3}{2}\right),$$
 * $$\left(±\frac{3+\sqrt5}{4},\,±\frac{7-\sqrt5}{4},\,±\frac{4-\sqrt5}{2},\,±\frac{3-\sqrt5}{2}\right),$$
 * $$\left(±\frac12,\,±\frac{1+\sqrt5}{2},\,±\frac{\sqrt5-1}{4},\,±\frac{5\sqrt5-7}{4}\right),$$
 * $$\left(±\frac12,\,±\frac{1+\sqrt5}{2},\,±3\frac{\sqrt5-1}{4},\,±3\frac{3-\sqrt5}{4}\right),$$
 * $$\left(±\frac12,\,±\frac{5+\sqrt5}{4},\,±(\sqrt5-2),\,±\frac{5-\sqrt5}{4}\right),$$
 * $$\left(±\frac12,\,±\frac{3-\sqrt5}{4},\,±(\sqrt5-2),\,±\frac{1+3\sqrt5}{4}\right),$$
 * $$\left(±\frac12,\,±\frac{5-\sqrt5}{4},\,±\frac{7-\sqrt5}{4},\,±\frac{5-\sqrt5}{2}\right),$$
 * $$\left(±\frac12,\,±\frac{\sqrt5-2}{2},\,±\frac{4-\sqrt5}{2},\,±\frac{2\sqrt5-1}{2}\right),$$
 * $$\left(±\frac12,\,±\frac{7-\sqrt5}{4},\,±(\sqrt5-1),\,±3\frac{\sqrt5-1}{4}\right),$$
 * $$\left(±\frac{1+\sqrt5}{2},\,±1,\,±(\sqrt5-2),\,±\frac{\sqrt5-1}{2}\right),$$
 * $$\left(±\frac{1+\sqrt5}{2},\,±\frac{\sqrt5-2}{2},\,±\frac{7-\sqrt5}{4},\,±\frac{7-3\sqrt5}{4}\right),$$
 * $$\left(±\frac{1+\sqrt5}{2},\,±\frac{5-\sqrt5}{4},\,±\frac{4-\sqrt5}{2},\,±\frac{3\sqrt5-5}{4}\right),$$
 * $$\left(±\frac{5+\sqrt5}{4},\,±\frac{\sqrt5-1}{4},\,±\frac{3-\sqrt5}{2},\,±\frac{2\sqrt5-3}{2}\right),$$
 * $$\left(±\frac{\sqrt5-1}{4},\,±\frac{3-\sqrt5}{4},\,±\frac{6-\sqrt5}{2},\,±\frac{\sqrt5-1}{2}\right),$$
 * $$\left(±\frac{\sqrt5-1}{4},\,±\frac32,\,±(\sqrt5-1),\,±\frac{3\sqrt5-5}{4}\right),$$
 * $$\left(±\frac{\sqrt5-1}{4},\,±\frac{3\sqrt5-1}{4},\,±\frac{\sqrt5-2}{2},\,±\frac{5-\sqrt5}{2}\right),$$
 * $$\left(±1,\,±\frac{3-\sqrt5}{4},\,±\frac{7-3\sqrt5}{4},\,±\frac{2\sqrt5-1}{2}\right),$$
 * $$\left(±1,\,±\frac32,\,±3\frac{3-\sqrt5}{4},\,±\frac{5-\sqrt5}{4}\right),$$
 * $$\left(±1,\,±\frac{5-\sqrt5}{4},\,±\frac{2\sqrt5-3}{2},\,±\frac{3\sqrt5-1}{4}\right),$$
 * $$\left(±\frac{\sqrt5}{2},\,±\frac{3-\sqrt5}{4},\,±\frac{5-\sqrt5}{2},\,±3\frac{\sqrt5-1}{4}\right),$$
 * $$\left(±\frac{\sqrt5}{2},\,±\frac32,\,±\frac{5-2\sqrt5}{2},\,±\frac{\sqrt5-2}{2}\right),$$
 * $$\left(±\frac{3-\sqrt5}{4},\,±3\frac{\sqrt5-1}{4},\,±\frac{3-\sqrt5}{2},\,±\frac{2\sqrt5-1}{2}\right),$$
 * $$\left(±\frac{1+3\sqrt5}{4},\,±\frac{\sqrt5-2}{2},\,±\frac{3-\sqrt5}{2},\,±\frac{3\sqrt5-5}{4}\right),$$
 * $$\left(±\frac{\sqrt5-1}{2},\,±\frac{5-\sqrt5}{4},\,±\frac{2\sqrt5-1}{2},\,±\frac{3\sqrt5-5}{4}\right),$$
 * $$\left(±\frac{\sqrt5-1}{2},\,±\frac{3\sqrt5-1}{4},\,±3\frac{\sqrt5-1}{4},\,±\frac{4-\sqrt5}{2}\right),$$
 * $$\left(±\frac{5-\sqrt5}{4},\,±\frac{3\sqrt5-1}{4},\,±\frac{\sqrt5-2}{2},\,±(\sqrt5-1)\right).$$

Related polychora
The great skewverted hexacositrishecatonicosachoron is the colonel of a regiment of 15 members, including three other Wythoffians, namely the great skewverted ditrigonal hexacositrishecatonicosachoron, great skewverted ditrigonal prismatohexacosidishecatonicosachoron, and great skewverted dishexacosidishecatonicosachoron.