Hecatonicosihexacositruncated hecatonicosihexacosichoron

The hecatonicosihexacositruncated hecatonicosihexacosichoron, or hixthix, is a nonconvex uniform polychoron that consists of 600 truncated tetrahedra, 120 truncated dodecahedra, and 120 icosidodecatruncated icosidodecahedra. 1 truncated tetrahedron, 1 truncated dodecahedron, and 2 icosidodecatruncated icosidodecahedra join at each vertex.

Vertex coordinates
The vertices of a hecatonicosihexacositruncated hecatonicosihexacosichoron of edge length 1 are given by all even permutations of:
 * $$\left(0,\,±\frac12,\,±\frac{13+3\sqrt5}{4},\,±\frac{3+2\sqrt5}{2}\right),$$
 * $$\left(0,\,±\frac{3-\sqrt5}{4},\,±\frac{11+5\sqrt5}{4},\,±\frac{1+2\sqrt5}{2}\right),$$
 * $$\left(0,\,±\frac12,\,±3\frac{5+\sqrt5}{4},\,±\frac{5+3\sqrt5}{4}\right),$$
 * $$\left(0,\,±\frac12,\,±\frac{9+5\sqrt5}{4},\,±\frac{3+5\sqrt5}{4}\right),$$
 * $$\left(0,\,±\frac{\sqrt5-1}{2},\,±(3+\sqrt5),\,±(1+\sqrt5)\right),$$
 * $$\left(±\frac{3-\sqrt5}{4},\,±\frac12,\,±\frac{1+3\sqrt5}{4},\,±\frac{5+3\sqrt5}{2}\right),$$
 * $$\left(±\frac{3-\sqrt5}{4},\,±\frac{3+\sqrt5}{4},\,±\frac{5+3\sqrt5}{2},\,±\frac32\right),$$
 * $$\left(±\frac{3-\sqrt5}{4},\,±\frac{2+\sqrt5}{2},\,±\frac{7+5\sqrt5}{4},\,±\frac{5+\sqrt5}{2}\right),$$
 * $$\left(±\frac{3-\sqrt5}{4},\,±\frac{4+\sqrt5}{2},\,±3\frac{3+|sqrt5}{4},\,±\frac{5+\sqrt5}{2}\right),$$
 * $$\left(±\frac12,\,±\frac{5-\sqrt5}{4},\,±\frac{5+\sqrt5}{4},\,±\frac{5+3\sqrt5}{2}\right),$$
 * $$\left(±\frac12,\,±\frac{5-\sqrt5}{4},\,±\frac{11+3\sqrt5}{4},\,±(2+\sqrt5)\right),$$
 * $$\left(±\frac12,\,±1,\,±\frac{7+5\sqrt5}{4},\,±5\frac{1+\sqrt5}{4}\right),$$
 * $$\left(±\frac12,\,±\frac{3+\sqrt5}{4},\,±\frac{3\sqrt5-1}{4},\,±\frac{5+3\sqrt5}{2}\right),$$
 * $$\left(±\frac12,\,±\frac{3+\sqrt5}{4},\,±3\frac{5+\sqrt5}{4},\,±\frac{3+\sqrt5}{2}\right),$$
 * $$\left(±\frac12,\,±\frac{3\sqrt5-1}{4},\,±(3+\sqrt5),\,±\frac{5+3\sqrt5}{4}\right),$$
 * $$\left(±\frac12,\,±\frac{7+\sqrt5}{4},\,±\frac{11+3\sqrt5}{4},\,±\frac{5+\sqrt5}{2}\right),$$
 * $$\left(±\frac12,\,±\frac{5+3\sqrt5}{4},\,±5\frac{1+\sqrt5}{4},\,±\frac{5+\sqrt5}{2}\right),$$
 * $$\left(±\frac{\sqrt5-1}{2},\,±1,\,±\frac{1+\sqrt5}{2},\,±\frac{5+3\sqrt5}{2}\right),$$
 * $$\left(±\frac{\sqrt5-1}{2},\,±\frac{3+\sqrt5}{2},\,±(2+\sqrt5),\,±\frac{5+\sqrt5}{2}\right),$$
 * $$\left(±\frac{5-\sqrt5}{4},\,±\frac{3+\sqrt5}{4},\,±\frac{7+5\sqrt5}{4},\,±3\frac{3+\sqrt5}{4}\right),$$
 * $$\left(±\frac{5-\sqrt5}{4},\,±\frac{3+\sqrt5}{4},\,±\frac{11+5\sqrt5}{4},\,±\frac{7+\sqrt5}{4}\right),$$
 * $$\left(±\frac{5-\sqrt5}{4},\,±\frac{1+\sqrt5}{2},\,±\frac{9+5\sqrt5}{4},\,±\frac{4+\sqrt5}{2}\right),$$
 * $$\left(±1,\,±\frac{3\sqrt5-1}{4},\,±\frac{11+5\sqrt5}{4},\,±\frac{2+\sqrt5}{2}\right),$$
 * $$\left(±1,\,±\frac32,\,±\frac{11+3\sqrt5}{4},\,±3\frac{3+\sqrt5}{4}\right),$$
 * $$\left(±1,\,±\frac{5+\sqrt5}{4},\,±\frac{13+3\sqrt5}{4},\,±\frac{4+\sqrt5}{2}\right),$$
 * $$\left(±\frac{3+\sqrt5}{4},\,±\frac32,\,±(2+\sqrt5),\,±5\frac{1+\sqrt5}{4}\right),$$
 * $$\left(±\frac{3+\sqrt5}{4},\,±\frac{1+\sqrt5}{2},\,±3\frac{5+\sqrt5}{4},\,±\frac{2+\sqrt5}{2}\right),$$
 * $$\left(±\frac{3+\sqrt5}{4},\,±\frac{1+3\sqrt5}{4},\,±\frac{13+3\sqrt5}{4},\,±\frac{5+3\sqrt5}{4}\right),$$
 * $$\left(±\frac{3\sqrt5-1}{4},\,±\frac{5+3\sqrt5}{4},\,±(2+\sqrt5),\,±\frac{4+\sqrt5}{2}\right),$$
 * $$\left(±\frac{3+\sqrt5}{4},\,±\frac{5+3\sqrt5}{4},\,±\frac{3+5\sqrt5}{4},\,±3\frac{3+\sqrt5}{4}\right),$$
 * $$\left(±\frac{3+\sqrt5}{4},\,±\frac{4+\sqrt5}{2},\,±(1+\sqrt5),\,±5\frac{1+\sqrt5}{4}\right),$$
 * $$\left(±\frac{3\sqrt5-1}{4},\,±\frac{3+\sqrt5}{2},\,±\frac{3+2\sqrt5}{2},\,±3\frac{3+\sqrt5}{4}\right),$$
 * $$\left(±\frac32,\,±\frac{5+\sqrt5}{4},\,±(3+\sqrt5),\,±\frac{7+\sqrt5}{4}\right),$$
 * $$\left(±\frac32,\,±\frac{1+3\sqrt5}{4},\,±\frac{9+5\sqrt5}{4},\,±\frac{3+\sqrt5}{2}\right),$$
 * $$\left(±\frac{1+\sqrt5}{2},\,±\frac{7+\sqrt5}{4},\,±\frac{3+2\sqrt5}{2},\,±5\frac{1+\sqrt5}{4}\right),$$
 * $$\left(±\frac{1+\sqrt5}{2},\,±\frac{1+2\sqrt5}{2},\,±\frac{11+3\sqrt5}{4},\,±\frac{5+3\sqrt5}{4}\right),$$
 * $$\left(±\frac{5+\sqrt5}{4},\,±\frac{2+\sqrt5}{2},\,±\frac{3+5\sqrt5}{4},\,±(2+\sqrt5)\right),$$
 * $$\left(±\frac{5+\sqrt5}{4},\,±\frac{3+\sqrt5}{2},\,±\frac{1+2\sqrt5}{2},\,±\frac{7+5\sqrt5}{4}\right),$$
 * $$\left(±\frac{1+3\sqrt5}{4},\,±\frac{2+\sqrt5}{2},\,±(1+\sqrt5),\,±\frac{11+3\sqrt5}{4}\right),$$
 * $$\left(±\frac{1+3\sqrt5}{4},\,±\frac{7+\sqrt5}{4},\,±\frac{5+3\sqrt5}{4},\,±\frac{7+5\sqrt5}{4}\right).$$