Great hexacosihecatonicosidishecatonicosachoron

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

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

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