Quasiprismatorhombated faceted hexacosichoron

The quasiprismatorhombated faceted hexacosichoron, or quippirfix, is a nonconvex uniform polychoron that consists of 1200 triangular prisms, 720 decagrammic prisms, 120 quasitruncated small stellated dodecahedra, and 120 small rhombicosidodecahedra. 1 triangular prism, 2 decagrammic prisms, 1 small rhombicosidodecahedron, and 1 quasitruncated small stellated dodecahedron join at each vertex. It can be obtained by quasiruncitruncating the small stellated hecatonicosachoron.

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

Related polychora
The quasiprismatorhombated faceted hexacosichoron is the colonel of a 3-member regiment that also includes the great prismatotrishecatonicosachoron and the rhombiprismic dishecatonicosachoron.