Hecatonicosihexacosidishecatonicosachoron

The hecatonicosihexacosidishecatonicosachoron, or hixady, is a nonconvex uniform polychoron that consists of 600 cuboctahedra, 120 truncated dodecahedra, 120 quasitruncated great stellated dodecahedra, and 120 quasitruncated dodecadodecahedra. 1 truncated dodecahedron, 1 quasitruncated great stellated dodecahedron, 1 cuboctahedron, and 2 quasitruncated dodecadodecahedra join at each vertex.

Vertex coordinates
The vertices of a hecatonicosihexacosidishecatonicosachoron of edge length 1 are given by all permutations of: Plus all even permutations of:
 * $$\left(0,\,±1,\,±2,\,±2\right),$$
 * $$\left(±\frac12,\,±\frac12,\,±\frac32,\,±\frac52\right),$$
 * $$\left(±1,\,±1,\,±\frac{3-\sqrt5}{2},\,±\frac{3+\sqrt5}{2}\right),$$
 * $$\left(±\frac{\sqrt5}{2},\,±\frac{\sqrt5}{2},\,±\frac12,\,±\frac52\right),$$
 * $$\left(±\frac32,\,±\frac32,\,±\frac{\sqrt5-2}{2},\,±\frac{2+\sqrt5}{2}\right),$$
 * $$\left(0,\,±\frac{\sqrt5-1}{4},\,±3\frac{1+\sqrt5}{4},\,±\frac{2\sqrt5-1}{2}\right),$$
 * $$\left(0,\,±\frac{3\sqrt5-5}{4},\,±\frac12,\,±\frac{5+3\sqrt5}{4}\right),$$
 * $$\left(0,\,±\frac{1+\sqrt5}{4},\,±\frac{1+2\sqrt5}{2},\,±3\frac{\sqrt5-1}{4}\right),$$
 * $$\left(0,\,±\frac{7-\sqrt5}{4},\,±\frac32,\,±\frac{7+\sqrt5}{4}\right),$$
 * $$\left(±\frac{\sqrt5-2}{2},\,±\frac{3-\sqrt5}{4},\,±\frac{5+3\sqrt5}{4},\,±\frac{\sqrt5-1}{2}\right),$$
 * $$\left(±\frac{\sqrt5-2}{2},\,±\frac{\sqrt5-1}{4},\,±\frac{3+\sqrt5}{2},\,±\frac{3\sqrt5-1}{4}\right),$$
 * $$\left(±\frac{\sqrt5-2}{2},\,±\frac12,\,±\frac{1+2\sqrt5}{2},\,±\frac{\sqrt5}{2}\right),$$
 * $$\left(±\frac{\sqrt5-2}{2},\,±\frac{3+\sqrt5}{4},\,±2,\,±\frac{5+\sqrt5}{4}\right),$$
 * $$\left(±\frac{3-\sqrt5}{4},\,±\frac{\sqrt5-1}{4},\,±\frac52,\,±\frac{1+\sqrt5}{2}\right),$$
 * $$\left(±\frac{3-\sqrt5}{4},\,±\frac{3-\sqrt5}{2},\,±\frac{5+3\sqrt5}{4},\,±\frac12\right),$$
 * $$\left(±\frac{3-\sqrt5}{4},\,±\frac12,\,±\sqrt5,\,±\frac{1+3\sqrt5}{4}\right),$$
 * $$\left(±\frac{3-\sqrt5}{4},\,±\frac{5-\sqrt5}{4},\,±\frac{2+\sqrt5}{2},\,±2\right),$$
 * $$\left(±\frac{3-\sqrt5}{4},\,±\frac{5-\sqrt5}{4},\,±\frac{1+2\sqrt5}{2},\,±1\right),$$
 * $$\left(±\frac{3-\sqrt5}{4},\,±3\frac{\sqrt5-1}{4},\,±\frac{\sqrt5}{2},\,±\frac{3+\sqrt5}{2}\right),$$
 * $$\left(±\frac{3-\sqrt5}{4},\,±1,\,±\frac{3+\sqrt5}{4},\,±\frac52\right),$$
 * $$\left(±\frac{3-\sqrt5}{4},\,±\frac{\sqrt5}{2},\,±2,\,±\frac{1+3\sqrt5}{4}\right),$$
 * $$\left(±\frac{3-\sqrt5}{4},\,±\frac{3+\sqrt5}{4},\,±\frac32,\,±\sqrt5\right),$$
 * $$\left(±\frac{3-\sqrt5}{2},\,±\frac12,\,±\frac{5+\sqrt5}{4},\,±\frac{7+\sqrt5}{4}\right),$$
 * $$\left(±\frac{3-\sqrt5}{2},\,±\frac{1+\sqrt5}{4},\,±\frac{2+\sqrt5}{2},\,±\frac{1+3\sqrt5}{4}\right),$$
 * $$\left(±\frac{3-\sqrt5}{2},\,±\frac{\sqrt5}{2},\,±\frac{3+\sqrt5}{4},\,±3\frac{1+\sqrt5}{4}\right),$$
 * $$\left(±\frac{3\sqrt5-5}{4},\,±\frac12,\,±\frac{3+\sqrt5}{2},\,±\frac{3+\sqrt5}{4}\right),$$
 * $$\left(±\frac{3\sqrt5-5}{4},\,±\frac{3+\sqrt5}{4},\,±\frac{2+\sqrt5}{2},\,±\frac{1+\sqrt5}{2}\right),$$
 * $$\left(±\frac12,\,±\frac{5-\sqrt5}{4},\,±\sqrt5,\,±\frac{5+\sqrt5}{4}\right),$$
 * $$\left(±\frac12,\,±\frac{5-\sqrt5}{4},\,±\frac{3+\sqrt5}{2},\,±\frac{7-\sqrt5}{4}\right),$$
 * $$\left(±\frac12,\,±\frac{\sqrt5}{2},\,±\frac{2+\sqrt5}{2},\,±\frac{2\sqrt5-1}{2}\right),$$
 * $$\left(±\frac12,\,±\frac{3+\sqrt5}{4},\,±\sqrt5,\,±\frac{3\sqrt5-1}{4}\right),$$
 * $$\left(±\frac{\sqrt5-1}{2},\,±\frac{5-\sqrt5}{4},\,±3\frac{1+\sqrt5}{4},\,±\frac32\right),$$
 * $$\left(±\frac{\sqrt5-1}{2},\,±\frac{1+\sqrt5}{4},\,±\frac52,\,±\frac{3+\sqrt5}{4}\right),$$
 * $$\left(±\frac{\sqrt5-1}{2},\,±1,\,±\sqrt5,\,±\frac{1+\sqrt5}{2}\right),$$
 * $$\left(±\frac{\sqrt5-1}{2},\,±\frac{\sqrt5}{2},\,±\frac{7+\sqrt5}{4},\,±\frac{3\sqrt5-1}{4}\right),$$
 * $$\left(±3\frac{\sqrt5-1}{4},\,±\frac32,\,±\frac{1+\sqrt5}{2},\,±\frac{5+\sqrt5}{4}\right),$$
 * $$\left(±1,\,±\frac{3+\sqrt5}{4},\,±\frac{5+\sqrt5}{4},\,±\frac{2\sqrt5-1}{2}\right),$$
 * $$\left(±1,\,±\frac{3\sqrt5-1}{4},\,±\frac32,\,±\frac{1+3\sqrt5}{4}\right),$$
 * $$\left(±\frac{\sqrt5}{2},\,±\frac{7-\sqrt5}{4},\,±\frac{1+3\sqrt5}{4},\,±\frac{1+\sqrt5}{2}\right),$$
 * $$\left(±\frac{\sqrt5}{2},\,±\frac{3+\sqrt5}{4},\,±2,\,±\frac{3\sqrt5-1}{4}\right).$$

Related polychora
The hecatonicosihexacosidishecatonicosachoron is the colonel of a 3-member regiment that also includes the hexacosihecatonicosidishecatonicosachoron and rhombic hexacosidishecatonicosachoron.