Quasitruncated small stellated hecatonicosachoron

The quasitruncated small stellated hecatonicosachoron, or quit sishi, is a nonconvex uniform polychoron that consists of 120 regular dodecahedra and 120 quasitruncated small stellated dodecahedra. One dodecahedron and three quasitruncate small stellated dodecahedra join at each vertex. As the name suggests, it can be obtained by quasitruncating the small stellated hecatonicosachoron.

Vertex coordinates
The vertices of a quasitruncated small stellated hecatonicosachoron of edge length 1 are all permutations of:

along with the even permutations of:
 * $$\left(±\frac{3-\sqrt5}{4},\,±\frac{3-\sqrt5}{4},\,±\frac{1+\sqrt5}{4},\,±\frac{5+\sqrt5}{4}\right),$$
 * $$\left(±\frac{\sqrt5-1}{4},\,±\frac{\sqrt5-1}{4},\,±\frac{\sqrt5-1}{4},\,±\frac{1+3\sqrt5}{4}\right),$$
 * $$\left(±\frac{\sqrt5-1}{4},\,±\frac{5-\sqrt5}{4},\,±\frac{3+\sqrt5}{4},\,±\frac{3+\sqrt5}{4}\right),$$
 * $$\left(±\frac12,\,±\frac12,\,±\frac{\sqrt5}{2},\,±\frac32\right),$$
 * $$\left(±\frac12,\,±\frac{\sqrt5}{2},\,±\frac{\sqrt5}{2},\,±\frac{\sqrt5}{2}\right),$$
 * $$\left(±\frac{1+\sqrt5}{4},\,±\frac{1+\sqrt5}{4}\,±\frac{1+|sqrt5}{4},\,±\frac{3\sqrt5-1}{4}\right),$$
 * $$\left(0,\,±\frac{3-\sqrt5}{4},\,±\frac{3+\sqrt5}{4},\,±\frac32\right),$$
 * $$\left(0,\,±\frac{3-\sqrt5}{4},\,±\frac{1+3\sqrt5}{4},\,±\frac12\right),$$
 * $$\left(0,\,±\frac{\sqrt5-1}{2},\,±\frac{1+\sqrt5}{2},\,±1\right),$$
 * $$\left(0,\,±\frac12,\,±\frac{3\sqrt5-1}{2},\,±\frac{3+\sqrt5}{4}\right),$$
 * $$\left(0,\,±\frac12,\,±\frac{5+\sqrt5}{4},\,±\frac{5-\sqrt5}{4}\right),$$
 * $$\left(±\frac{3-\sqrt5}{4},\,±\frac{\sqrt5-1}{4},\,±\frac{1+\sqrt5}{2},\,±\frac{\sqrt5}{2}\right),$$
 * $$\left(±\frac{3-\sqrt5}{4},\,±1,\,±\frac{\sqrt5}{2},\,±\frac{3+\sqrt5}{4}\right),$$
 * $$\left(±\frac{\sqrt5-1}{4},\,±\frac12,\,±\frac{\sqrt5-1}{2},\,±\frac{5+\sqrt5}{4}\right),$$
 * $$\left(±\frac{\sqrt5-1}{4},\,±1,\,±\frac32,\,±\frac{1+\sqrt5}{4}\right),$$
 * $$\left(±\frac12,\,±\frac{5-\sqrt5}{4},\,±\frac{1+\sqrt5}{4},\,±\frac{1+\sqrt5}{2}\right),$$
 * $$\left(±\frac{\sqrt5-1}{2},\,±\frac{1+\sqrt5}{4},\,±\frac{3+\sqrt5}{4},\,±\frac{\sqrt5}{2}\right).$$