Small hexacositrishecatonicosachoron

The small hexacositrishecatonicosachoron, or sixathi, is a nonconvex uniform polychoron that consists of 600 truncated tetrahedra, 120 quasitruncated small stellated dodecahedra, 120 small rhombicosidodecahedra, and 120 great quasitruncated icosidodecahedra. 1 truncated tetrahedron, 1 quasitruncated small stellated dodecahedron, 1 small rhombicosidodecahedron, and 2 great quasitruncated icosidodecahedra join at each vertex.

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

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