Great ditrigonal prismatotrishecatonicosachoron

The great ditrigonal prismatotrishecatonicosachoron, or gid tipathi, is a nonconvex uniform polychoron that consists of 1200 triangular prisms, 120 truncated icosahedra, 120 great ditrigonal dodecicosidodecahedra, and 120 great quasitruncated icosidodecahedra. 1 triangular prism, 1 truncated icosahedron, 1 great ditrigonal dodecicosidodecahedron, and 2 great quasitruncated icosidodecahedra join at each vertex.

Vertex coordinates
The vertices of a great ditrigonal prismatotrishecatonicosachoron of edge length 1 are given by all permutations of: Plus all even permutations of:
 * $$\left(±\frac12,\,±\frac12,\,±\frac{1+2\sqrt5}{2},\,±\frac{2\sqrt5-3}{2}\right),$$
 * $$\left(±1,\,±1,\,±\sqrt5,\,±(\sqrt5-1)\right),$$
 * $$\left(±\frac{2\sqrt5-1}{2},\,±\frac{2\sqrt5-1}{2},\,±\frac12,\,±\frac32\right),$$
 * $$\left(0,\,±\frac{3+\sqrt5}{2},\,±(\sqrt5-1),\,±\frac{3-\sqrt5}{2}\right),$$
 * $$\left(0,\,±\frac12,\,±3\frac{1+\sqrt5}{4},\,±5\frac{\sqrt5-1}{4}\right),$$
 * $$\left(0,\,±\frac{\sqrt5}{2},\,±\frac{3-\sqrt5}{4},\,±\frac{13-\sqrt5}{4}\right),$$
 * $$\left(0,\,±\frac{7+\sqrt5}{4},\,±\frac{2\sqrt5-1}{2},\,±\frac{3\sqrt5-5}{4}\right),$$
 * $$\left(0,\,±\frac{1+3\sqrt5}{4},\,±\frac{11-\sqrt5}{4},\,±\frac{\sqrt5-2}{2}\right),$$
 * $$\left(±\frac{2+\sqrt5}{2},\,±\frac{1+\sqrt5}{4},\,±1,\,±\frac{\sqrt5-1}{4}\right),$$
 * $$\left(±\frac{2+\sqrt5}{2},\,±\frac12,\,±\frac{4-\sqrt5}{2},\,±\frac{2\sqrt5-1}{2}\right),$$
 * $$\left(±\frac{2+\sqrt5}{2},\,±1,\,±\frac{9-\sqrt5}{4},\,±\frac{3\sqrt5-5}{4}\right),$$
 * $$\left(±\frac{2+\sqrt5}{2},\,±\frac{\sqrt5}{2},\,±\frac32,\,±\frac{2\sqrt5-3}{2}\right),$$
 * $$\left(±\frac{2+\sqrt5}{2},\,±\frac{3-\sqrt5}{4},\,±2,\,±\frac{7-3\sqrt5}{4}\right),$$
 * $$\left(±\frac{1+\sqrt5}{4},\,±\frac{3+\sqrt5}{2},\,±\frac{2\sqrt5-3}{2},\,±\frac{5-\sqrt5}{4}\right),$$
 * $$\left(±\frac{1+\sqrt5}{4},\,±2,\,±\frac{2\sqrt5-1}{2},\,±3\frac{\sqrt5-1}{4}\right),$$
 * $$\left(±\frac{1+\sqrt5}{4},\,±\frac12,\,±\frac{13-\sqrt5}{4},\,±\frac{\sqrt5-1}{2}\right),$$
 * $$\left(±\frac{1+\sqrt5}{4},\,±\frac{\sqrt5-2}{2},\,±\frac{9-\sqrt5}{4},\,±\sqrt5\right),$$
 * $$\left(±\frac{3+\sqrt5}{2},\,±\frac12,\,±\frac{7-\sqrt5}{4},\,±\frac{7-3\sqrt5}{4}\right),$$
 * $$\left(±\frac12,\,±\frac{1+\sqrt5}{2},\,±3\frac{\sqrt5-1}{4},\,±\frac{11-\sqrt5}{4}\right),$$
 * $$\left(±\frac12,\,±\frac{1+\sqrt5}{2},\,±5\frac{\sqrt5-1}{4},\,±\frac{5+\sqrt5}{4}\right),$$
 * $$\left(±\frac12,\,±\frac{5+\sqrt5}{4},\,±\sqrt5,\,±\frac{7-3\sqrt5}{4}\right),$$
 * $$\left(±\frac12,\,±1,\,±\frac{13-\sqrt5}{4},\,±\frac{3-\sqrt5}{4}\right),$$
 * $$\left(±\frac12,\,±\frac{1+2\sqrt5}{2},\,±\frac{\sqrt5-2}{2},\,±\frac{4-\sqrt5}{2}\right),$$
 * $$\left(±\frac12,\,±2,\,±\frac{9-\sqrt5}{4},\,±\frac{7-\sqrt5}{4}\right),$$
 * $$\left(±\frac{1+\sqrt5}{2},\,±\frac{7+\sqrt5}{4},\,±\frac{2\sqrt5-3}{2},\,±\frac{3-\sqrt5}{4}\right),$$
 * $$\left(±\frac{1+\sqrt5}{2},\,±\frac{3-\sqrt5}{4},\,±\frac{9-\sqrt5}{4},\,±\frac{2\sqrt5-1}{2}\right),$$
 * $$\left(±\frac{1+\sqrt5}{2},\,±\frac{\sqrt5-1}{2},\,±2,\,±(\sqrt5-1)\right),$$
 * $$\left(±\frac{5+\sqrt5}{4},\,±1,\,±\frac{2\sqrt5-3}{2},\,±\frac{1+3\sqrt5}{4}\right),$$
 * $$\left(±\frac{5+\sqrt5}{4},\,±\frac32,\,±\frac{9-\sqrt5}{4},\,±\frac{3-\sqrt5}{2}\right),$$
 * $$\left(±\frac{5+\sqrt5}{4},\,±\frac{5-\sqrt5}{4},\,±2,\,±\frac{4-\sqrt5}{2}\right),$$
 * $$\left(±3\frac{1+\sqrt5}{4},\,±1,\,±\frac{4-\sqrt5}{2},\,±3\frac{\sqrt5-1}{4}\right),$$
 * $$\left(±3\frac{1+\sqrt5}{4},\,±\frac32,\,±\frac{7-3\sqrt5}{4},\,±\frac{\sqrt5-1}{2}\right),$$
 * $$\left(±1,\,±\frac{7+\sqrt5}{4},\,±\frac{4-\sqrt5}{2},\,±\frac{7-\sqrt5}{4}\right),$$
 * $$\left(±1,\,±\frac{3-\sqrt5}{4},\,±\frac{7-3\sqrt5}{4},\,±\frac{1+2\sqrt5}{2}\right),$$
 * $$\left(±1,\,±\frac32,\,±\frac{11-\sqrt5}{4},\,±\frac{5-\sqrt5}{4}\right),$$
 * $$\left(±\frac{\sqrt5}{2},\,±\sqrt5,\,±3\frac{\sqrt5-1}{4},\,±\frac{7-\sqrt5}{4}\right),$$
 * $$\left(±\frac{3-\sqrt5}{4},\,±\frac{1+2\sqrt5}{2},\,±3\frac{\sqrt5-1}{4},\,±\frac{3-\sqrt5}{2}\right),$$
 * $$\left(±\frac{3-\sqrt5}{4},\,±\frac{5-\sqrt5}{4},\,±\sqrt5,\,±\frac{2\sqrt5-1}{2}\right),$$
 * $$\left(±\frac{1+3\sqrt5}{4},\,±\frac{\sqrt5-1}{2},\,±\frac{7-\sqrt5}{4},\,±\frac{2\sqrt5-1}{2}\right),$$
 * $$\left(±\frac{\sqrt5-1}{2},\,±\frac{1+2\sqrt5}{2},\,±\frac{3\sqrt5-5}{4},\,±\frac{5-\sqrt5}{4}\right),$$

Related polychora
The great ditrigonal prismatotrishecatonicosachoron is the colonel of a 3-member regiment that also includes the great prismatohecatonicosihexacosihecatonicosachoron and great small hexacosidishecatonicosachoron.