Rectified hecatonicosachoric prism

The rectified hecatonicosachoric prism or rahipe is a prismatic uniform polyteron that consists of 2 rectified hecatonicosachora, 120 icosidodecahedral prisms, and 600 tetrahedral prisms. 1 rectified hecatonicosachoron, 2 tetrahedral prisms, and 3 icosidodecahedraal prisms join at each vertex. As the name suggests, it is a prism based on the rectified hecatonicosachoron, which also makes it a convex segmentoteron.

Vertex coordinates
The vertices of a rectified hecatonicosachoric prism of edge length 1 are given by all permutations of the first four coordinates of:

along with all even permutations of the first four coordinates of:
 * $$\left(0,\,0,\,±\frac{1+\sqrt5}{2},\,±(2+\sqrt5),\,±\frac12\right),$$
 * $$\left(0,\,±\frac{3+\sqrt5}{2},\,±\frac{3+\sqrt5}{2},\,±\frac{3+\sqrt5}{2},\,±\frac12\right),$$
 * $$\left(±\frac{3+\sqrt5}{4},\,±\frac{3+\sqrt5}{4},\,±\frac{3+\sqrt5}{4},\,±3\frac{3+\sqrt5}{4},\,±\frac12\right),$$
 * $$\left(±\frac{3+\sqrt5}{4},\,±\frac{3+\sqrt5}{4},\,±\frac{5+3\sqrt5}{4},\,±\frac{5+3\sqrt5}{4},\,±\frac12\right),$$


 * $$\left(0,\,±\frac12,\,±\frac{7+3\sqrt5}{4},\,±\frac{5+3\sqrt5}{4},\,±\frac12\right),$$
 * $$\left(0,\,±\frac{1+\sqrt5}{4},\,±3\frac{3+\sqrt5}{4},\,±\frac{2+\sqrt5}{2},\,±\frac12\right),$$
 * $$\left(±\frac12,\,±\frac{1+\sqrt5}{4},\,±(2+\sqrt5),\,±\frac{3+\sqrt5}{4},\,±\frac12\right),$$
 * $$\left(±\frac12,\,±\frac{3+\sqrt5}{4},\,±\frac{7+3\sqrt5}{4},\,±\frac{3+\sqrt5}{2},\,±\frac12\right),$$
 * $$\left(±\frac{1+\sqrt5}{4},\,±\frac{2+\sqrt5}{2},\,±\frac{5+3\sqrt5}{4},\,±\frac{3+\sqrt5}{2},\,±\frac12\right),$$
 * $$\left(±\frac{3+\sqrt5}{4},\,±\frac{1+\sqrt5}{2},\,±\frac{7+3\sqrt5}{4},\,±\frac{2+\sqrt5}{2},\,±\frac12\right).$$