Small hecatonicosihecatonicosachoron

The small hecatonicosihecatonicosachoron, or shihi, is a nonconvex uniform polychoron that consists of 120 truncated dodecahedra and 120 truncated great dodecahedra. 2 of each join at each vertex.

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

Vertex coordinates
Coordinates for the vertices of a small hecatonicosihecatonicosachoron of edge length 1 are given by all permutations of: together with all even permutations of:
 * $$\left(0,\,0,\,±\frac{3+\sqrt5}{2},\,±(3+\sqrt5)\right),$$
 * $$\left(±\frac{3+\sqrt5}{4},\,±\frac{3+\sqrt5}{4},\,±\frac{\sqrt5-1}{4},\,±\frac{11+5\sqrt5}{4}\right),$$
 * $$\left(±\frac{3+\sqrt5}{2},\,±\frac{3+\sqrt5}{2},\,±\frac{1+\sqrt5}{2},\,±(2+\sqrt5)\right),$$
 * $$\left(±\frac{3+\sqrt5}{4},\,±\frac{3+\sqrt5}{4},\,±3\frac{3+\sqrt5}{4},\,±3\frac{3+\sqrt5}{4}\right),$$
 * $$\left(±\frac{5+3\sqrt5}{4},\,±\frac{5+3\sqrt5}{4},\,±\frac{3+\sqrt5}{4},\,±3\frac{3+\sqrt5}{4}\right),$$
 * $$\left(0,\,±\frac{\sqrt5-1}{4},\,±\frac{5+2\sqrt5}{2},\,±\frac{7+3\sqrt5}{4}\right),$$
 * $$\left(0,\,±\frac12,\,±\frac{5+\sqrt5}{4},\,±\frac{11+5\sqrt5}{4}\right),$$
 * $$\left(0,\,±\frac12,\,±\frac{9+5\sqrt5}{4},\,±\frac{5+3\sqrt5}{4}\right),$$
 * $$\left(0,\,±\frac{5+3\sqrt5}{4},\,±\frac{3+2\sqrt5}{2},\,±\frac{7+3\sqrt5}{4}\right),$$
 * $$\left(±\frac{\sqrt5-1}{4},\,±\frac{2+\sqrt5}{2},\,±(2+\sqrt5),\,±\frac{7+3\sqrt5}{4}\right),$$
 * $$\left(±\frac12,\,±\frac{1+\sqrt5}{4},\,±\frac{1+\sqrt5}{2},\,±\frac{11+5\sqrt5}{4}\right),$$
 * $$\left(±\frac12,\,±\frac{1+\sqrt5}{4},\,±(2+\sqrt5),\,±3\frac{3+\sqrt5}{4}\right),$$
 * $$\left(±\frac12,\,±\frac{3+\sqrt5}{4},\,±\frac{9+5\sqrt5}{4},\,±\frac{3+\sqrt5}{2}\right),$$
 * $$\left(±\frac12,\,±\frac{3+\sqrt5}{2},\,±3\frac{3+\sqrt5}{4},\,±\frac{7+3\sqrt5}{2}\right),$$
 * $$\left(±\frac{1+\sqrt5}{4},\,±\frac{3+\sqrt5}{4},\,±(2+\sqrt5),\,±\frac{3+2\sqrt5}{2}\right),$$
 * $$\left(±\frac{1+\sqrt5}{4},\,±\frac{3+\sqrt5}{4},\,±(3+\sqrt5),\,±\frac{2+\sqrt5}{2}\right),$$
 * $$\left(±\frac{1+\sqrt5}{4},\,±\frac{1+\sqrt5}{2},\,±\frac{5+2\sqrt5}{2},\,±\frac{5+3\sqrt5}{4}\right),$$
 * $$\left(±\frac{3+\sqrt5}{4},\,±\frac{1+\sqrt5}{2},\,±\frac{9+5\sqrt5}{4},\,±\frac{2+\sqrt5}{2}\right),$$
 * $$\left(±\frac{3+\sqrt5}{4},\,±\frac{5+\sqrt5}{4},\,±\frac{5+2\sqrt5}{2},\,±\frac{3+\sqrt5}{2}\right),$$
 * $$\left(±\frac{3+\sqrt5}{4},\,±\frac{3+\sqrt5}{2},\,±\frac{7+3\sqrt5}{4},\,±\frac{3+2\sqrt5}{2}\right),$$
 * $$\left(±\frac{1+\sqrt5}{2},\,±\frac{2+\sqrt5}{2},\,±\frac{7+3\sqrt5}{4},\,±3\frac{3+\sqrt5}{4}\right),$$
 * $$\left(±\frac{5+\sqrt5}{4},\,±\frac{2+\sqrt5}{2},\,±\frac{5+3\sqrt5}{4},\,±(2+\sqrt5)\right).$$