Dishecatonicosachoron

The dishecatonicosachoron, or dahi, is a nonconvex uniform polychoron that consists of 120 truncated icosahedra and 120 truncated great icosahedra. 2 of each join at each vertex.

It is the medial stage of the truncation series between a grand hecatonicosachoron and its dual great stellated hecatonicosachoron, which makes it the bitruncation of both of these polychora.

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