Hecatonicosihexacositruncated hexacosihecatonicosachoron

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

Vertex coordinates
The vertices of a hecatonicosihexacositruncated hexacosihecatonicosachoron of edge length 1 are given by all permutations of: plus all even permutations of:
 * $$\left(±\frac12,\,±\frac12,\,±\frac{\sqrt5-2}{2},\,±\frac{3+2\sqrt5}{2}\right),$$
 * $$\left(±\frac{3+\sqrt5}{4},\,±\frac{3+\sqrt5}{4},\,±\frac{\sqrt5-1}{4},\,±\frac{11+\sqrt5}{4}\right),$$
 * $$\left(±\frac32,\,±\frac32,\,±\frac12,\,±\frac{4+\sqrt5}{2}\right),$$
 * $$\left(±\frac{5+\sqrt5}{4},\,±\frac{5+\sqrt5}{4},\,±\frac{3-\sqrt5}{4},\,±\frac{9+\sqrt5}{4}\right),$$
 * $$\left(±\frac{5+\sqrt5}{4},\,±\frac{5+\sqrt5}{4},\,±\frac{3\sqrt5-1}{4},\,±3\frac{1+\sqrt5}{4}\right),$$
 * $$\left(±\frac{1+3\sqrt5}{4},\,±\frac{1+3\sqrt5}{4},\,±\frac{3+\sqrt5}{4},\,±\frac{7+\sqrt5}{4}\right),$$
 * $$\left(0,\,±\frac{3-\sqrt5}{4},\,±\frac{3+2\sqrt5}{2},\,±\frac{5-\sqrt5}{4}\right),$$
 * $$\left(0,\,±\frac12,\,±\frac{11+\sqrt5}{4},\,±\frac{5+\sqrt5}{4}\right),$$
 * $$\left(0,\,±\frac{5-\sqrt5}{4},\,±\frac{7+3\sqrt5}{4},\,±\frac32\right),$$
 * $$\left(0,\,±\frac{1+\sqrt5}{2},\,±\frac{3+\sqrt5}{2},\,±\sqrt5\right),$$
 * $$\left(0,\,±\frac{5+\sqrt5}{4},\,±\frac{1+2\sqrt5}{2},\,±\frac{1+3\sqrt5}{4}\right),$$
 * $$\left(±\frac{\sqrt5-2}{2},\,±\frac12,\,±\frac{4+\sqrt5}{2},\,±\frac{2+\sqrt5}{2}\right),$$
 * $$\left(±\frac{\sqrt5-2}{2},\,±1,\,±\frac{7+3\sqrt5}{4},\,±\frac{3+\sqrt5}{4}\right),$$
 * $$\left(±\frac{\sqrt5-2}{2},\,±\frac{3+\sqrt5}{4},\,±\frac{3+\sqrt5}{2},\,±3\frac{1+\sqrt5}{4}\right),$$
 * $$\left(±\frac{\sqrt5-2}{2},\,±\frac{1+\sqrt5}{2},\,±\frac{5+\sqrt5}{4},\,±\frac{5+3\sqrt5}{4}\right),$$
 * $$\left(±\frac{3-\sqrt5}{4},\,±\frac{\sqrt5-1}{4},\,±\frac{3+2\sqrt5}{2},\,±\frac{\sqrt5-1}{2}\right),$$
 * $$\left(±\frac{3-\sqrt5}{4},\,±\frac12,\,±(1+\sqrt5),\,±\frac{1+3\sqrt5}{4}\right),$$
 * $$\left(±\frac{3-\sqrt5}{4},\,±\frac{1+\sqrt5}{4},\,±\frac{9+\sqrt5}{4},\,±3\frac{1+\sqrt5}{4}\right),$$
 * $$\left(±\frac{3-\sqrt5}{4},\,±\frac{1+\sqrt5}{4},\,±\frac{7+3\sqrt5}{4},\,±\frac{3\sqrt5-1}{4}\right),$$
 * $$\left(±\frac{3-\sqrt5}{4},\,±\frac{3+\sqrt5}{4},\,±\frac232,\,±(1+\sqrt5)\right),$$
 * $$\left(±\frac{3-\sqrt5}{4},\,±\frac32,\,±\frac{3+\sqrt5}{2},\,±\frac{7+\sqrt5}{4}\right),$$
 * $$\left(±\frac{\sqrt5-1}{4},\,±\frac{5-\sqrt5}{4},\,±\frac{5+3\sqrt5}{4},\,±\frac{7+\sqrt5}{4}\right),$$
 * $$\left(±\frac{\sqrt5-1}{4},\,±1,\,±\frac{1+2\sqrt5}{2},\,±3\frac{1+\sqrt5}{4}\right),$$
 * $$\left(±\frac{\sqrt5-1}{4},\,±\frac{3\sqrt5-1}{4},\,±\frac{1+\sqrt5}{2},\,±\frac{4+\sqrt5}{2}\right),$$
 * $$\left(±\frac12,\,±\frac{5-\sqrt5}{4},\,±(1+\sqrt5),\,±\frac{5+\sqrt5}{4}\right),$$
 * $$\left(±\frac12,\,±\frac{1+\sqrt5}{4},\,±\frac{5+3\sqrt5}{4},\,±\sqrt5\right),$$
 * $$\left(±\frac12,\,±\frac{1+\sqrt5}{4},\,±\frac{11+\sqrt5}{4},\,±\frac{1+\sqrt5}{2}\right),$$
 * $$\left(±\frac12,\,±1,\,±\frac{9+\sqrt5}{4},\,±\frac{7+\sqrt5}{4}\right),$$
 * $$\left(±\frac12,\,±\frac{3+\sqrt5}{4},\,±(1+\sqrt5),\,±\frac{3\sqrt5-1}{4}\right),$$
 * $$\left(±\frac12,\,±\frac32,\,±\frac{1+2\sqrt5}{2},\,±\frac{2+\sqrt5}{2}\right),$$
 * $$\left(±\frac12,\,±\frac{1+\sqrt5}{2},\,±\frac{9+\sqrt5}{4},\,±\frac{1+3\sqrt5}{4}\right),$$
 * $$\left(±\frac{\sqrt5-1}{2},\,±\frac{1+\sqrt5}{4},\,±\frac{4+\sqrt5}{2},\,±\frac{1+3\sqrt5}{4}\right),$$
 * $$\left(±\frac{\sqrt5-1}{2},\,±1,\,±(1+\sqrt5),\,±\frac{1+\sqrt5}{2}\right),$$
 * $$\left(±\frac{\sqrt5-1}{2},\,±\frac{3+\sqrt5}{4},\,±\frac{9+\sqrt5}{4},\,±\frac{2+\sqrt5}{2}\right),$$
 * $$\left(±\frac{\sqrt5-1}{2},\,±\frac32,\,±\frac{5+3\sqrt5}{4},\,±\frac{5+\sqrt5}{4}\right),$$
 * $$\left(±\frac{5-\sqrt5}{4},\,±1,\,±\frac{4+\sqrt5}{2},\,±\frac{5+\sqrt5}{4}\right),$$
 * $$\left(±\frac{5-\sqrt5}{4},\,±\frac{3+\sqrt5}{4},\,±\frac{5+3\sqrt5}{4},\,±\frac{1+3\sqrt5}{4}\right),$$
 * $$\left(±\frac{3+\sqrt5}{4},\,±\frac{5+\sqrt5}{4},\,±\sqrt5,\,±\frac{2+\sqrt5}{2}\right),$$
 * $$\left(±\frac{3\sqrt5-1}{4},\,±\frac{1+\sqrt5}{2},\,±\frac{7+\sqrt5}{4},\,±\frac{2+\sqrt5}{2}\right),$$
 * $$\left(±\frac32,\,±\frac{1+\sqrt5}{2},\,±3\frac{1+\sqrt5}{4},\,±\frac{1+3\sqrt5}{4}\right).$$

Related polychora
The hecatonicosihexacositruncated hexacosihecatonicosachoron is the colonel of a 3-member regiment that also includes the great hexacositrishecatonicosachoron and great rhombic trishecatonicosachoron.