Swirlprismatic hecatonicosihexacosichoron

The swirlprismatic hecatonicosihexacosichoron, or sphix, is a uniform polychoron in the small stellated hecatonicosachoron's regiment. Its cells are 600 pentagrammic prisms and 120 pentagonal prisms, with 50 and 10 of each, respectively, meeting each of the polychoron's 120 vertices.

Vertex coordinates
The vertices of a swirlprismatic hecatonicosihexacosichoron of unit edge length are given by: and all even permutations of: The first two sets of vertices form a unit icositetrachoron that can be inscribed into the small stellated hecatonicosachoron. This corresponds to the fact there is a compound of 25 icositetrachora with the same vertices and edges as the small stellated hecatonicosachoron.
 * $$\left(±1,\,0,\,0,\,0\right),$$
 * $$\left(±\frac12,\,±\frac12,\,±\frac12,\,±\frac12\right),$$
 * $$\left(±\frac{1+\sqrt5}{4},\,±\frac{\sqrt5-1}{4},\,±\frac12,\,0\right).$$