Dishecatonicosaquasitruncated dishecatonicosachoron

The dishecatonicosiquasitruncated dishecatonicosachoron, or dahiquatady, is a nonconvex uniform polychoron that consists of 120 quasitruncated small stellated dodecahedra, 120 truncated icosahedra, and 120 icosidodecatruncated icosidodecahedra. 1 quasitruncated small stellated dodecahedron, 1 truncated icosahedron, and 2 icosidodecatruncated icosidodecahedra join at each vertex.

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