Small hecatonicosihecatonicosihexacosichoron

The small hecatonicosihecatonicosihexacosichoron, or shihix, is a nonconvex uniform polychoron that consists of 600 regular tetrahedra, 120 great stellated dodecahedra, and 120 small icosicosidodecahedra. 1 tetrahedron, 1 great stellated dodecahedron, and 3 small icosicosidodecahedra join at each vertex.

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

Related polychora
The small hecatonicosihecatonicosihexacosichoron is the colonel of a regiment of 7 members. Its other members include the small hexacosihecatonicosidishecatonicosachoron, hecatonicosihecatonicosintercepted hecatonicosachoron, small hecatonicosafaceted hecatonicosihexacosihecatonicosachoron, small hexacosifaceted trishecatonicosachoron, small spinohexacosidishecatonicosachoron, and small spinohecatonicosidishecatonicosachoron.