Hecatonicosachoric prism

The hecatonicosachoric prism or hipe is a prismatic uniform polyteron that consists of 2 hecatonicosachora and 120 dodecahedral prisms. 1 hecatonicosachoron and 4 dodecahedral prisms join at each vertex. As the name suggests, it is a prism based on the hecatonicosachoron, which also makes it a convex segmentoteron.

Vertex coordinates
The vertices of a hecantonicosachoric prism of edge length 1 are given by all permutations of the first four coordinates of: together with all the even permutations of the first four coordinates of:
 * $$\left(±\frac{3+\sqrt{5}}{2},\,±\frac{3+\sqrt{5}}{2},\,0,\,0,\,±\frac12\right),$$
 * $$\left(±\frac{5+3\sqrt{5}}{4},\,±\frac{3+\sqrt{5}}{4},\,±\frac{3+\sqrt{5}}{4},\,±\frac{3+\sqrt{5}}{4},\,±\frac12\right),$$
 * $$\left(±\frac{2+\sqrt{5}}{2},\,±\frac{2+\sqrt{5}}{2},\,±\frac{2+\sqrt{5}}{2},\,±\frac{1}{2},\,±\frac12\right),$$
 * $$\left(±\frac{7+3\sqrt{5}}{4},\,±\frac{1+\sqrt{5}}{4},\,±\frac{1+\sqrt{5}}{4},\,±\frac{1+\sqrt{5}}{4},\,±\frac12\right),$$
 * $$\left(±\frac{7+3\sqrt{5}}{4},\,±\frac{3+\sqrt{5}}{4},\,±\frac{1}{2},\,0,\,±\frac12\right),$$
 * $$\left(±\frac{2+\sqrt{5}}{2},\,±\frac{5+3\sqrt{5}}{4},\,0,\,±\frac{1+\sqrt{5}}{4},\,±\frac12\right),$$
 * $$\left(±\frac{2+\sqrt{5}}{2},\,±\frac{3+\sqrt{5}}{4},\,±\frac{3+\sqrt{5}}{2},\,±\frac{1+\sqrt{5}}{4},\,±\frac12\right),$$