Great tritrigonary hexacositrishecatonicosachoron

The great tritrigonary hexacositrishecatonicosachoron, or getit xethi, is a nonconvex uniform polychoron that consists of 600 regular tetrahedra, 120 quasitruncated great stellated dodecahedra, 120 great dodecicosidodecahedra, and 120 small ditrigonary icosidodecahedra. 1 tetrahedron, 3 quasitruncated great stellated dodecahedra, 3 great dodecicosidodecahedra, and 1 small ditrigonary icosidodecahedron join at each vertex.

The great tritrigonary hexacositrishecatonicosachoron contains the vertices of an inscribed great quasitruncated icosidodecahedral prism.

Vertex coordinates
The vertices of a great tritrigonary hexacositrishecatonicosachoron of edge length 1 are all permutations of: along with the even permutations of:
 * $$\left(0,\,±1,\,±\frac{3-\sqrt5}{2},\,±\frac{3-\sqrt5}{2}\right),$$
 * $$\left(±\frac12,\,±\frac12,\,±\frac12,\,±\frac{2\sqrt5-3}{2}\right),$$
 * $$\left(±\frac12,\,±\frac12,\,±\frac{\sqrt5-2}{2},\,±\frac{4-\sqrt5}{2}\right),$$
 * $$\left(±\frac{\sqrt5-1}{2},\,±\frac{\sqrt5-1}{2},\,±\frac{\sqrt5-1}{2},\,±\frac{3-\sqrt5}{2}\right),$$
 * $$\left(±\frac{\sqrt5-2}{2},\,±\frac{\sqrt5-2}{2},\,±\frac{\sqrt5-2}{2},\,±\frac{\sqrt5}{2}\right),$$
 * $$\left(0,\,±\frac{1+\sqrt5}{4},\,±\frac{\sqrt5-1}{4},\,±\frac{2\sqrt5-3}{2}\right),$$
 * $$\left(0,\,±\frac12,\,±\frac{3\sqrt5-5}{4},\,±3\frac{\sqrt5-1}{4}\right),$$
 * $$\left(0,\,±\frac{\sqrt5}{2},\,±\frac{5-\sqrt5}{4},\,±\frac{7-3\sqrt5}{4}\right),$$
 * $$\left(0,\,±\frac{3-\sqrt5}{4},\,±\frac{5-\sqrt5}{4},\,±\frac{4-\sqrt5}{2}\right),$$
 * $$\left(±\frac{1+\sqrt5}{4},\,±\frac12,\,±\frac{7-3\sqrt5}{4},\,±\frac{\sqrt5-1}{2}\right),$$
 * $$\left(±\frac{1+\sqrt5}{4},\,±\frac{5-\sqrt5}{4},\,±\frac{3-\sqrt5}{2},\,±\frac{\sqrt5-2}{2}\right),$$
 * $$\left(±\frac12,\,±1,\,±\frac{7-3\sqrt5}{4},\,±\frac{3-\sqrt5}{4}\right),$$
 * $$\left(±\frac12,\,±\frac{3-\sqrt5}{4},\,±\frac{3-\sqrt5}{2},\,±3\frac{\sqrt5-1}{4}\right),$$
 * $$\left(±\frac12,\,±\frac{\sqrt5-1}{2},\,±\frac{5-\sqrt5}{4},\,±\frac{3\sqrt5-5}{4}\right),$$
 * $$\left(±\frac{\sqrt5-1}{4},\,±1,\,±\frac{3\sqrt5-5}{4},\,±\frac{\sqrt5-2}{2}\right),$$
 * $$\left(±\frac{\sqrt5-1}{4},\,±\frac{3-\sqrt5}{4},\,±\frac{4-\sqrt5}{2},\,±\frac{\sqrt5-1}{2}\right),$$
 * $$\left(±\frac{3-\sqrt5}{4},\,±\frac{\sqrt5-1}{2},\,±\frac{\sqrt5-2}{2},\,±3\frac{\sqrt5-1}{4}\right).$$

Related polychora
The great tritrigonary hexacositrishecatonicosachoron is the colonel of a regiment that contains 79 uniform members as well as 30 fissary uniforms.