Small dishecatonicosaquasitruncated prismatodishecatonicosachoron

The small dishecatonicosiquasitruncated prismatodishecatonicosachoron, or sidhiquit paddy, is a nonconvex uniform polychoron that consists of 720 decagonal prisms, 120 great rhombicosidodecahedra, 120 quasitruncated dodecadodecahedra, and 120 icosidodecatruncated icosidodecahedra. 1 of each type of cell join at each vertex.

Vertex coordinates
Vertex coordinates for a small dishecatonicosiquasitruncated prismatodishecatonicosachoron of edge length 1 are given by all permutations of: plus all even permutations of:
 * $$\left(±\frac{3-\sqrt5}{4},\,±\frac{3-\sqrt5}{4},\,±3\frac{1+\sqrt5}{4},\,±\frac{9+5\sqrt5}{4}\right),$$
 * $$\left(±\frac{3-\sqrt5}{4},\,±\frac{3-\sqrt5}{4},\,±\frac{7+3\sqrt5}{4},\,±\frac{11+3\sqrt5}{4}\right),$$
 * $$\left(±\frac12,\,±\frac12,\,±\frac32,\,±\frac{4+3\sqrt5}{2}\right),$$
 * $$\left(±\frac12,\,±\frac12,\,±\frac{3+2\sqrt5}{2},\,±\frac{6+\sqrt5}{2}\right),$$
 * $$\left(±\frac{\sqrt5}{2},\,±\frac{\sqrt5}{2},\,±\frac12,\,±\frac{4+3\sqrt5}{2}\right),$$
 * $$\left(±\frac{3+\sqrt5}{4},\,±\frac{3+\sqrt5}{4},\,±\frac{1+3\sqrt5}{4},\,±\frac{13+3\sqrt5}{4}\right),$$
 * $$\left(±\frac{3+\sqrt5}{4},\,±\frac{3+\sqrt5}{4},\,±\frac{3+5\sqrt5}{4},\,±3\frac{3+\sqrt5}{4}\right),$$
 * $$\left(±\frac32,\,±\frac32,\,±\frac{2+\sqrt5}{2},\,±\frac{5+2\sqrt5}{2}\right),$$
 * $$\left(±\frac{1+3\sqrt5}{4},\,±\frac{1+3\sqrt5}{4},\,±\frac{5+3\sqrt5}{4},\,±3\frac{3+\sqrt5}{4}\right),$$
 * $$\left(±3\frac{1+\sqrt5}{4},\,±3\frac{1+\sqrt5}{4},\,±\frac{5+\sqrt5}{4},\,±5\frac{1+\sqrt5}{4}\right),$$
 * $$\left(±\frac{5+3\sqrt5}{4},\,±\frac{5+3\sqrt5}{4},\,±\frac{3+\sqrt5}{4},\,±\frac{3+5\sqrt5}{4}\right),$$
 * $$\left(±\frac{7+3\sqrt5}{4},\,±\frac{7+3\sqrt5}{4},\,±\frac{3-\sqrt5}{4},\,±\frac{9+\sqrt5}{4}\right),$$
 * $$\left(±\frac{7+3\sqrt5}{4},\,±\frac{7+3\sqrt5}{4},\,±\frac{3\sqrt5-1}{4},\,±3\frac{1+\sqrt5}{4}\right),$$
 * $$\left(±\frac{3+2\sqrt5}{2},\,±\frac{3+2\sqrt5}{2},\,±\frac{\sqrt5}{2},\,±\frac32\right),$$
 * $$\left(±3\frac{3+\sqrt5}{4},\,±3\frac{3+\sqrt5}{4},\,±\frac{\sqrt5-1}{4},\,±\frac{5-\sqrt5}{4}\right),$$
 * $$\left(±\frac{3-\sqrt5}{4},\,±\frac{\sqrt5-1}{4},\,±\frac{4+3\sqrt5}{2},\,±\frac{1+\sqrt5}{2}\right),$$
 * $$\left(±\frac{3-\sqrt5}{4},\,±\frac12,\,±\frac{3+\sqrt5}{2},\,±\frac{13+3\sqrt5}{4}\right),$$
 * $$\left(±\frac{3-\sqrt5}{4},\,±\frac12,\,±(1+\sqrt5),\,±\frac{7+5\sqrt5}{4}\right),$$
 * $$\left(±\frac{3-\sqrt5}{4},\,±\frac12,\,±(3+\sqrt5),\,±\frac{1+3\sqrt5}{4}\right),$$
 * $$\left(±\frac{3-\sqrt5}{4},\,±\frac{\sqrt5-1}{2},\,±\frac{5+3\sqrt5}{4},\,±\frac{5+2\sqrt5}{2}\right),$$
 * $$\left(±\frac{3-\sqrt5}{4},\,±1,\,±\frac{3+\sqrt5}{4},\,±\frac{4+3\sqrt5}{2}\right),$$
 * $$\left(±\frac{3-\sqrt5}{4},\,±\frac{3+\sqrt5}{4},\,±\frac32,\,±(3+\sqrt5)\right),$$
 * $$\left(±\frac{3-\sqrt5}{4},\,±\frac{5+\sqrt5}{4},\,±\frac{7+3\sqrt5}{4},\,±5\frac{1+\sqrt5}{4}\right),$$
 * $$\left(±\frac{3-\sqrt5}{4},\,±\frac{1+3\sqrt5}{4},\,±\frac{4+\sqrt5}{2},\,±(2+\sqrt5)\right),$$
 * $$\left(±\frac{3-\sqrt5}{4},\,±\frac{5+3\sqrt5}{4},\,±\frac{4+\sqrt5}{2},\,±\frac{5+\sqrt5}{2}\right),$$
 * $$\left(±\frac{\sqrt5-1}{4},\,±1,\,±\frac{3+2\sqrt5}{2},\,±5\frac{1+\sqrt5}{4}\right),$$
 * $$\left(±\frac{\sqrt5-1}{4},\,±\frac{3+\sqrt5}{4},\,±\frac{7+\sqrt5}{4},\,±\frac{13+3\sqrt5}{4}\right),$$
 * $$\left(±\frac{\sqrt5-1}{4},\,±\frac{3\sqrt5-1}{4},\,±\frac{3+\sqrt5}{2},\,±\frac{5+2\sqrt5}{2}\right),$$
 * $$\left(±\frac12,\,±\frac{5-\sqrt5}{4},\,±(3+\sqrt5),\,±\frac{5+\sqrt5}{4}\right),$$
 * $$\left(±\frac12,\,±\frac{1+\sqrt5}{4},\,±\frac{3+5\sqrt5}{4},\,±(2+\sqrt5)\right),$$
 * $$\left(±\frac12,\,±1,\,±3\frac{1+\sqrt5}{4},\,±\frac{13+3\sqrt5}{4}\right),$$
 * $$\left(±\frac12,\,±\frac{\sqrt5}{2},\,±\frac{1+2\sqrt5}{2},\,±\frac{5+2\sqrt5}{2}\right),$$
 * $$\left(±\frac12,\,±\frac{3+\sqrt5}{4},\,±2,\,±\frac{9+5\sqrt5}{4}\right),$$
 * $$\left(±\frac12,\,±\frac{3+\sqrt5}{4},\,±\frac{5+\sqrt5}{2},\,±5\frac{1+\sqrt5}{4}\right),$$
 * $$\left(±\frac12,\,±\frac{3+\sqrt5}{4},\,±(3+\sqrt5),\,±\frac{3\sqrt5-1}{4}\right),$$
 * $$\left(±\frac12,\,±\frac{1+\sqrt5}{2},\,±\frac{9+\sqrt5}{4},\,±\frac{7+5\sqrt5}{4}\right),$$
 * $$\left(±\frac12,\,±2,\,±\frac{7+3\sqrt5}{4},\,±3\frac{3+\sqrt5}{4}\right),$$
 * $$\left(±\frac12,\,±\frac{2+\sqrt5}{2},\,±\frac{4+\sqrt5}{2},\,±\frac{6+\sqrt5}{2}\right),$$
 * $$\left(±\frac12,\,±\frac{3+\sqrt5}{2},\,±\frac{7+3\sqrt5}{4},\,±\frac{3+5\sqrt5}{4}\right),$$
 * $$\left(±\frac12,\,±\frac{1+2\sqrt5}{2},\,±\frac{4+\sqrt5}{2},\,±\frac{3+2\sqrt5}{2}\right),$$
 * $$\left(±\frac{\sqrt5-1}{2},\,±\frac{1+\sqrt5}{4},\,±\frac{4+3\sqrt5}{2},\,±\frac{3+\sqrt5}{4}\right),$$
 * $$\left(±\frac{\sqrt5-1}{2},\,±1,\,±(3+\sqrt5),\,±\frac{1+\sqrt5}{2}\right),$$
 * $$\left(±\frac{\sqrt5-1}{2},\,±\frac{7+\sqrt5}{4},\,±\frac{7+3\sqrt5}{4},\,±\frac{3+2\sqrt5}{2}\right),$$
 * $$\left(±\frac{\sqrt5-1}{2},\,±3\frac{1+\sqrt5}{4},\,±\frac{4+\sqrt5}{2},\,±3\frac{3+\sqrt5}{4}\right),$$
 * $$\left(±\frac{5-\sqrt5}{4},\,±1,\,±\frac{2+\sqrt5}{2},\,±\frac{9+5\sqrt5}{4}\right),$$
 * $$\left(±\frac{5-\sqrt5}{4},\,±\frac{\sqrt5}{2},\,±\frac{7+3\sqrt5}{4},\,±(2+\sqrt5)\right),$$
 * $$\left(±\frac{5-\sqrt5}{4},\,±\frac{3+\sqrt5}{4},\,±\frac{5+3\sqrt5}{4},\,±\frac{7+5\sqrt5}{4}\right),$$
 * $$\left(±\frac{1+\sqrt5}{4},\,±\frac{3\sqrt5-1}{4},\,±\frac{5+\sqrt5}{4},\,±\frac{9+5\sqrt5}{4}\right),$$
 * $$\left(±\frac{1+\sqrt5}{4},\,±\frac32,\,±\frac{5+\sqrt5}{2},\,±3\frac{3+\sqrt5}{4}\right),$$
 * $$\left(±\frac{1+\sqrt5}{4},\,±\frac{5+\sqrt5}{4},\,±\frac{9+\sqrt5}{4},\,±\frac{11+3\sqrt5}{4}\right),$$
 * $$\left(±1,\,±\frac{\sqrt5}{2},\,±\frac{1+3\sqrt5}{4},\,±\frac{9+5\sqrt5}{4}\right),$$
 * $$\left(±1,\,±\frac{3+\sqrt5}{4},\,±\frac{7+3\sqrt5}{4},\,±\frac{6+\sqrt5}{2}\right),$$
 * $$\left(±1,\,±\frac{3+\sqrt5}{2},\,±\frac{5+\sqrt5}{2},\,±(1+\sqrt5)\right),$$
 * $$\left(±1,\,±\frac32,\,±\frac{5+3\sqrt5}{4},\,±\frac{11+3\sqrt5}{4}\right),$$
 * $$\left(±1,\,±\frac{9+\sqrt5}{4},\,±\frac{3+2\sqrt5}{2},\,±\frac{5+3\sqrt5}{4}\right),$$
 * $$\left(±\frac{\sqrt5}{2},\,±\frac{1+\sqrt5}{2},\,±\frac{5+\sqrt5}{4},\,±\frac{13+3\sqrt5}{4}\right),$$
 * $$\left(±\frac{\sqrt5}{2},\,±\frac{1+3\sqrt5}{4},\,±\frac{3+\sqrt5}{2},\,±\frac{11+3\sqrt5}{4}\right),$$
 * $$\left(±\frac{\sqrt5}{2},\,±\frac{7+\sqrt5}{4},\,±\frac{5+\sqrt5}{2},\,±\frac{7+3\sqrt5}{4}\right),$$
 * $$\left(±\frac{\sqrt5}{2},\,±\frac{3+\sqrt5}{2},\,±\frac{9+\sqrt5}{4},\,±3\frac{3+\sqrt5}{4}\right),$$
 * $$\left(±\frac{3+\sqrt5}{4},\,±\frac{1+\sqrt5}{2},\,±\frac{1+2\sqrt5}{2},\,±\frac{11+3\sqrt5}{4}\right),$$
 * $$\left(±\frac{3+\sqrt5}{4},\,±\frac{5+\sqrt5}{4},\,±2,\,±\frac{5+2\sqrt5}{2}\right),$$
 * $$\left(±\frac{3+\sqrt5}{4},\,±\frac{1+3\sqrt5}{4},\,±\frac{7+\sqrt5}{4},\,±\frac{7+5\sqrt5}{4}\right),$$
 * $$\left(±\frac{3+\sqrt5}{4},\,±2,\,±\frac{3+2\sqrt5}{2},\,±\frac{7+3\sqrt5}{4}\right),$$
 * $$\left(±\frac{3+\sqrt5}{4},\,±3\frac{1+\sqrt5}{4},\,±\frac{3+\sqrt5}{2},\,±\frac{6+\sqrt5}{2}\right),$$
 * $$\left(±\frac{3+\sqrt5}{4},\,±\frac{1+2\sqrt5}{2},\,±\frac{7+3\sqrt5}{4},\,±(1+\sqrt5)\right),$$
 * $$\left(±\frac{3\sqrt5-1}{4},\,±\frac{3+\sqrt5}{2},\,±\frac{5+3\sqrt5}{4},\,±\frac{3+2\sqrt5}{2}\right),$$
 * $$\left(±\frac32,\,±\frac{1+\sqrt5}{2},\,±3\frac{1+\sqrt5}{4},\,±\frac{7+5\sqrt5}{4}\right),$$
 * $$\left(±\frac32,\,±\frac{5+\sqrt5}{4},\,±3\frac{3+\sqrt5}{4},\,±(1+\sqrt5)\right),$$
 * $$\left(±\frac32,\,±\frac{7+\sqrt5}{4},\,±(2+\sqrt5),\,±3\frac{1+\sqrt5}{4}\right),$$
 * $$\left(±\frac{1+\sqrt5}{2},\,±\frac{5+\sqrt5}{4},\,±\frac{6+\sqrt5}{2},\,±\frac{5+3\sqrt5}{4}\right),$$
 * $$\left(±\frac{1+\sqrt5}{2},\,±2,\,±(2+\sqrt5),\,±\frac{3+\sqrt5}{2}\right),$$
 * $$\left(±\frac{1+\sqrt5}{2},\,±\frac{2+\sqrt5}{2},\,±\frac{3+5\sqrt5}{4},\,±\frac{7+3\sqrt5}{4}\right),$$
 * $$\left(±\frac{1+\sqrt5}{2},\,±3\frac{1+\sqrt5}{4},\,±\frac{1+2\sqrt5}{2},\,±3\frac{3+\sqrt5}{4}\right),$$
 * $$\left(±\frac{5+\sqrt5}{4},\,±\frac{1+3\sqrt5}{4},\,±\frac{3+2\sqrt5}{2},\,±(1+\sqrt5)\right),$$
 * $$\left(±\frac{1+3\sqrt5}{4},\,±\frac{2+\sqrt5}{2},\,±5\frac{1+\sqrt5}{4},\,±\frac{3+\sqrt5}{2}\right).$$