Great hexacosihecatonicosihecatonicosachoron

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

Vertex coordinates
The vertices of a great hexacosihecatonicosihecatonicosachoron of edge length 1 are all permutations of:

along with the even permutations of:
 * $$\left(±\frac12,\,±\frac12,\,±\frac{\sqrt5-2}{2},\,±\frac{5-2\sqrt5}{2}\right),$$
 * $$\left(±\frac{\sqrt5-1}{4},\,±\frac{\sqrt5-1}{4},\,±\frac{\sqrt5-1}{4},\,±\frac{5\sqrt5-9}{4}\right),$$
 * $$\left(±\frac{\sqrt5-1}{4},\,±\frac{5-\sqrt5}{4},\,±\frac{7-3\sqrt5}{4},\,±\frac{7-3\sqrt5}{4}\right),$$
 * $$\left(±\frac{3-\sqrt5}{4},\,±\frac{3-\sqrt5}{4},\,±\frac{3\sqrt5-5}{4},\,±3\frac{3-\sqrt5}{4}\right),$$
 * $$\left(±\frac{3-\sqrt5}{4},\,±\frac{3\sqrt5-5}{4},\,±\frac{3\sqrt5-5}{4},\,±\frac{3\sqrt5-5}{4}\right),$$
 * $$\left(±\frac{\sqrt5-2}{2},\,±\frac{\sqrt5-2}{2},\,±\frac{\sqrt5-2}{2},\,±\frac{2\sqrt5-3}{2}\right),$$
 * $$\left(0,\,±\frac12,\,±\frac{7-3\sqrt5}{4},\,±3\frac{3-\sqrt5}{4}\right),$$
 * $$\left(0,\,±\frac12,\,±\frac{5\sqrt5-9}{4},\,±\frac{3-\sqrt5}{4}\right),$$
 * $$\left(0,\,±\frac{\sqrt5-1}{2},\,±(\sqrt5-2),\,±\frac{3-\sqrt5}{2}\right),$$
 * $$\left(0,\,±\frac{3-\sqrt5}{4},\,±\frac{2\sqrt5-3}{2},\,±\frac{7-3\sqrt5}{4}\right),$$
 * $$\left(0,\,±\frac{3-\sqrt5}{4},\,±\frac{5-2\sqrt5}{2},\,±\frac{5-\sqrt5}{4}\right),$$
 * $$\left(±\frac12,\,±\frac{\sqrt5-1}{4},\,±(\sqrt5-2),\,±\frac{3\sqrt5-5}{4}\right),$$
 * $$\left(±\frac12,\,±\frac{3-\sqrt5}{2},\,±\frac{3\sqrt5-5}{4},\,±\frac{7-3\sqrt5}{4}\right),$$
 * $$\left(±\frac{\sqrt5-1}{4},\,±\frac{3-\sqrt5}{4},\,±\frac{\sqrt5-1}{2},\,±\frac{5-2\sqrt5}{2}\right),$$
 * $$\left(±\frac{\sqrt5-1}{4},\,±\frac{3-\sqrt5}{2},\,±3\frac{3-\sqrt5}{4},\,±\frac{\sqrt5-2}{2}\right),$$
 * $$\left(±\frac{3-\sqrt5}{4},\,±\frac{5-\sqrt5}{4},\,±\frac{\sqrt5-2}{2},\,±(\sqrt5-2)\right),$$
 * $$\left(±\frac{\sqrt5-1}{2},\,±\frac{\sqrt5-2}{2},\,±\frac{7-3\sqrt5}{4},\,±\frac{3\sqrt5-5}{4}\right).$$

Related polychora
The great hexacosihecatonicosihecatonicosachoron is the colonel of a regiment of 7 members. Its other members include the quasidisprismatohexacosihecatonicosachoron, diprismatohecatonicosachoron, great hecatonicosafaceted prismatohecatonicosihexacosichoron, great hexacosifaceted prismatodishecatonicosachoron, great spinoprismatohexacosihecatonicosachoron, and great spinoprismatodishecatonicosachoron.