Small dishexacosidishecatonicosachoron

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

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

Related polychora
The small dishexacosidishecatonicosachoron is the colonel of a regiment of 7 members. Its other members include the small hexacosifaceted hexacosidishecatonicosachoron, small hecatonicosafaceted hexacosidishecatonicosachoron, small ditrigonal hecatonicosihexacosihecatonicosachoron, hecatonicosihecatonicosihexacosichoron, small spinotrishecatonicosachoron, and small spinohecatonicosidishexacosichoron.