Pentagonal-prismatic heptacosiicosachoron

The pentagonal-prismatic heptacosiicosachoron, or paphacki, is a noble uniform polychoron in the small stellated hecatonicosachoron's regiment. It consists of 720 pentagonal prisms, 60 of which meet at each of its 120 vertices.

Vertex coordinates
The vertices of a pentagonal-prismatic heptacosiicosachoron 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.
 * $$\left(±1,\,0,\,0,\,0\right),$$
 * $$\left(±\frac12,\,±\frac12,\,±\frac12,\,±\frac12\right),$$
 * $$\left(±\frac{1+\sqrt5}{4},\,±\frac{\sqrt5-1}{4},\,±\frac12,\,0\right).$$