Great ditrigonal hecatonicosihexacosihecatonicosachoron

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

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

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