Rectified hexacosichoric prism

The rectified hexacosichoric prism or roxip is a prismatic uniform polyteron that consists of 2 rectified hexacosichora, 120 icosahedral prisms, and 600 octahedral prisms. 1 rectified hexacosichoron, 2 icosahedral prisms, and 5 octahedral prisms join at each vertex. As the name suggests, it is a prism based on the rectified hexacosichoron, which also makes it a convex segmentoteron.

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

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