Hecatonicosihecatonicosaquasitruncated dishecatonicosachoron

The hecatonicosihecatonicosiquasitruncated dishecatonicosachoron, or hihiquatady, is a nonconvex uniform polychoron that consists of 120 truncated dodecahedra, 120 quasitruncated great stellated dodecahedra, and 120 icosidodecatruncated icosidodecahedra. 1 truncated dodecahedron, 1 quasitruncated great stellated dodecahedron, and 2 icosidodecatruncated icosidodecahedra join at each vertex.

Vertex coordinates
The vertices of a hecatonicosihecatonicosiquasitruncated dishecatonicosachoron of edge length 1 are given by all even permutations of:
 * $$\left(0,\,±\frac{3\sqrt5-1}{4},\,±\frac{3+5\sqrt5}{4},\,±\frac12\right),$$
 * $$\left(0,\,±\frac12,\,±\frac{5\sqrt5-3}{4},\,±\frac{5+3\sqrt5}{4}\right),$$
 * $$\left(0,\,±1,\,±(\sqrt5-1),\,±(1+\sqrt5)\right),$$
 * $$\left(0,\,±\frac{7-\sqrt5}{4},\,±\frac{7+\sqrt5}{4},\,±\frac52\right),$$
 * $$\left(0,\,±\frac32,\,±\frac{9+\sqrt5}{4},\,±\frac{9-\sqrt5}{4}\right),$$
 * $$\left(±\frac{\sqrt5-2}{2},\,±\frac{3-\sqrt5}{4},\,±\frac{\sqrt5-1}{2},\,±\frac{3+5\sqrt5}{4}\right),$$
 * $$\left(±\frac{\sqrt5-2}{2},\,±\frac12,\,±\frac{2\sqrt5-1}{2},\,±\frac{4+\sqrt5}{2}\right),$$
 * $$\left(±\frac{\sqrt5-2}{2},\,±\frac{5-\sqrt5}{4},\,±\frac{3\sqrt5-1}{4},\,±(1+\sqrt5)\right),$$
 * $$\left(±\frac{\sqrt5-2}{2},\,±\frac32,\,±\frac{2+\sqrt5}{2},\,±\frac52\right),$$
 * $$\left(±\frac{\sqrt5-2}{2},\,±\frac{9-\sqrt5}{4},\,±\frac{5+\sqrt5}{4},\,±\frac{3+\sqrt5}{2}\right),$$
 * $$\left(±\frac{3-\sqrt5}{4},\,±\frac{3-\sqrt5}{2},\,±\frac12,\,±\frac{3+5\sqrt5}{4}\right),$$
 * $$\left(±\frac{3-\sqrt5}{4},\,±\frac12,\,±\frac{1+3\sqrt5}{4},\,±3\right),$$
 * $$\left(±\frac{3-\sqrt5}{4},\,±\frac{5-\sqrt5}{4},\,±\sqrt5,\,±\frac{1+2\sqrt5}{2}\right),$$
 * $$\left(±\frac{3-\sqrt5}{4},\,±\frac{4-\sqrt5}{2},\,±\frac{3+\sqrt5}{4},\,±(1+\sqrt5)\right),$$
 * $$\left(±\frac{3-\sqrt5}{4},\,±\frac{4-\sqrt5}{2},\,±\frac{7+\sqrt5}{4},\,±\frac{3+\sqrt5}{2}\right),$$
 * $$\left(±\frac{3-\sqrt5}{4},\,±(\sqrt5-1),\,±\frac{4+\sqrt5}{2},\,±\frac{3+\sqrt5}{4}\right),$$
 * $$\left(±\frac{3-\sqrt5}{4},\,±\frac{3+\sqrt5}{4},\,±\frac32,\,±3\right),$$
 * $$\left(±\frac{3-\sqrt5}{4},\,±\frac{3+\sqrt5}{4},\,±\sqrt5,\,±\frac52\right),$$
 * $$\left(±\frac{3-\sqrt5}{4},\,±\frac{1+\sqrt5}{2},\,±\frac{1+2\sqrt5}{2},\,±\frac{9-\sqrt5}{4}\right),$$
 * $$\left(±\frac{3-\sqrt5}{2},\,±\frac{5-\sqrt5}{4}<\,±\frac{2+\sqrt5}{2},\,±\frac{9+\sqrt5}{4}\right),$$
 * $$\left(±\frac{3-\sqrt5}{2},\,±1,\,±\sqrt5,\,±\frac{3+\sqrt5}{2}\right),$$
 * $$\left(±\frac{3-\sqrt5}{2},\,±\frac{7-\sqrt5}{4},\,±\frac{3+\sqrt5}{4},\,±\frac{4+\sqrt5}{2}\right),$$
 * $$\left(±\frac{3-\sqrt5}{2},\,±\frac{3\sqrt5-1}{4},\,±\frac{5+3\sqrt5}{4},\,±\frac32\right),$$
 * $$\left(±\frac{3\sqrt5-5}{4},\,±\frac{5-\sqrt5}{4},\,±\frac{1+\sqrt5}{2},\,±\frac{4+\sqrt5}{2}\right),$$
 * $$\left(±\frac{3\sqrt5-5}{4},\,±\frac32,\,±\frac{1+3\sqrt5}{4},\,±\frac{3+\sqrt5}{2}\right),$$
 * $$\left(±\frac12,\,±\frac{5-\sqrt5}{4},\,±\frac{5+\sqrt5}{4},\,±3\right),$$
 * $$\left(±\frac12,\,±\frac{4-\sqrt5}{2},\,±\frac{2+\sqrt5}{2},\,±\frac{1+2\sqrt5}{2}\right),$$
 * $$\left(±\frac12,\,±\frac{4-\sqrt5}{2},\,±\frac32,\,±\frac{4+\sqrt5}{2}\right),$$
 * $$\left(±\frac12,\,±\frac{3+\sqrt5}{4},\,±\frac{3\sqrt5-1}{4},\,±3\right),$$
 * $$\left(±\frac12,\,±\frac{3+\sqrt5}{4},\,±\frac{5\sqrt5-3}{4},\,±\frac{3+\sqrt5}{2}\right),$$
 * $$\left(±\frac12,\,±\frac32,\,±\frac{2\sqrt5-1}{2},\,±\frac{1+2\sqrt5}{2}\right),$$
 * $$\left(±\frac{\sqrt5-1}{2},\,±\frac{4-\sqrt5}{2},\,±\frac{5+\sqrt5}{4},\,±\frac{5+3\sqrt5}{4}\right),$$
 * $$\left(±\frac{\sqrt5-1}{2},\,±1,\,±\frac{1+\sqrt5}{2},\,±3\right),$$
 * $$\left(±\frac{\sqrt5-1}{2},\,±\frac{7-\sqrt5}{4},\,±\frac{1+3\sqrt5}{4},\,±\frac{1+2\sqrt5}{2}\right),$$
 * $$\left(±\frac{\sqrt5-1}{2},\,±\frac{3+\sqrt5}{4},\,±\frac{3+\sqrt5}{4},\,±\frac{2\sqrt5-1}{2},\,±\frac{9+\sqrt5}{4}\right),$$
 * $$\left(±(\sqrt5-1),\,±\frac{5+\sqrt5}{4},\,±\frac{1+3\sqrt5}{4},\,±\frac{2+\sqrt5}{2}\right),$$
 * $$\left(±\frac{3+\sqrt5}{4},\,±\frac{1+\sqrt5}{2},\,±\frac{5\sqrt5-3}{4},\,±\frac{2+\sqrt5}{2}\right),$$
 * $$\left(±\frac{3+\sqrt5}{4},\,±\frac{2\sqrt5-1}{2},\,±\sqrt5,\,±\frac{5+\sqrt5}{4}\right),$$
 * $$\left(±\frac{3\sqrt5-1}{4},\,±\frac32,\,±\frac{1+3\sqrt5}{4},\,±\sqrt5\right),$$
 * $$\left(±\frac{3\sqrt5-1}{4},\,±\frac{1+\sqrt5}{2},\,±\frac{2\sqrt5-1}{2},\,±\frac{7+\sqrt5}{4}\right).$$