Small tritrigonary prismatohecatonicosidishexacosichoron

The small tritrigonary prismatohecatonicosidishexacosichoron, or stut phiddix, is a nonconvex uniform polychoron that consists of 600 regular tetrahedra, 720 pentagrammic prisms, 600 cuboctahedra, and 120 small ditrigonary icosidodecahedra. 1 tetrahedron, 3 pentagrammic prisms, 3 cuboctahedra, and 1 small ditrigonary icosidodecahedron join at each vertex.

It can be constructed from the small ditetrahedronary hexacosihecatonicosachoron by expanding its small ditrigonary icosidodecahedral cells outward.

The small tritrigonary prismatohecatonicosidishexacosichoron contains the vertices of an inscribed great rhombicosidodecahedral prism.

Vertex coordinates
The vertices of a small tritrigonary prismatohecatonicosidishexacosichoron of edge length 1 are all permutations of: along with the even permutations of:
 * $$\left(0,\,±1,\,±\frac{3+\sqrt5}{2},\,±\frac{3+\sqrt5}{2}\right),$$
 * $$\left(±\frac12,\,±\frac12,\,±\frac12,\,±\frac{3+2\sqrt5}{2}\right),$$
 * $$\left(±\frac12,\,±\frac12,\,±\frac{2+\sqrt5}{2},\,±\frac{4+\sqrt5}{2}\right),$$
 * $$\left(±\frac{1+\sqrt5}{2},\,±\frac{1+\sqrt5}{2},\,±\frac{1+\sqrt5}{2},\,±\frac{3+\sqrt5}{2}\right),$$
 * $$\left(±\frac{2+\sqrt5}{2},\,±\frac{2+\sqrt5}{2},\,±\frac{2+\sqrt5}{2},\,±\frac{\sqrt5}{2}\right),$$
 * $$\left(0,\,±\frac{\sqrt5-1}{4},\,±\frac{1+\sqrt5}{4},\,±\frac{3+2\sqrt5}{2}\right),$$
 * $$\left(0,\,±\frac12,\,±\frac{5+3\sqrt5}{4},\,±3\frac{1+\sqrt5}{4}\right),$$
 * $$\left(0,\,±\frac{\sqrt5}{2},\,±\frac{5+\sqrt5}{4},\,±\frac{7+3\sqrt5}{4}\right),$$
 * $$\left(0,\,±\frac{3+\sqrt5}{4},\,±\frac{5+\sqrt5}{4},\,±\frac{4+\sqrt5}{2}\right),$$
 * $$\left(±\frac{\sqrt5-1}{4},\,±\frac12,\,±\frac{7+3\sqrt5}{4},\,±\frac{1+\sqrt5}{2}\right),$$
 * $$\left(±\frac{\sqrt5-1}{4},\,±\frac{5+\sqrt5}{4},\,±\frac{3+\sqrt5}{2},\,±\frac{2+\sqrt5}{2}\right),$$
 * $$\left(±\frac12,\,±1,\,±\frac{7+3\sqrt5}{4},\,±\frac{3+\sqrt5}{4}\right),$$
 * $$\left(±\frac12,\,±\frac{3+\sqrt5}{4},\,±\frac{3+\sqrt5}{2},\,±3\frac{1+\sqrt5}{4}\right),$$
 * $$\left(±\frac12,\,±\frac{1+\sqrt5}{2},\,±\frac{5+\sqrt5}{4},\,±\frac{5+3\sqrt5}{4}\right),$$
 * $$\left(±\frac{1+\sqrt5}{4},\,±1,\,±\frac{5+3\sqrt5}{4},\,±\frac{2+\sqrt5}{2}\right),$$
 * $$\left(±\frac{1+\sqrt5}{4},\,±\frac{3+\sqrt5}{4},\,±\frac{4+\sqrt5}{2},\,±\frac{1+\sqrt5}{2}\right),$$
 * $$\left(±\frac{3+\sqrt5}{4},\,±\frac{1+\sqrt5}{2},\,±\frac{2+\sqrt5}{2},\,±3\frac{1+\sqrt5}{4}\right).$$

Related polychora
The small tritrigonary prismatohecatonicosidishexacosichoron is the colonel of a regiment that contains 79 uniform members as well as 30 fissary uniforms.