Small rhombated hexacosichoric prism

The small rhombated hexacosichoric prism or srixip is a prismatic uniform polyteron that consists of 2 small rhombated hexacosichora, 120 icosidodecahedral prisms, 600 cuboctahedral prisms, and 720 square-pentagonal duoprisms. 1 small rhombated hexacosichoron, 1 icosidodecahedral prism, 2 cuboctahedral prisms, and 2 square-pentagonal duopriss join at each vertex. As the name suggests, it is a prism based on the small rhombated hexacosichoron, which also makes it a convex segmentoteron.

Vertex coordinates
Coordinates for the vertices of a small rhombated hexacosichoric prism of edge length 1 are given by all permutations of the first four coordinates: together with all even permutations of the first four coordinates of:
 * $$\left(0,\,0,\,±\frac{1+\sqrt5}{2},\,±\frac{5+3\sqrt5}{2},\,±\frac12\right),$$
 * $$\left(0,\,±1,\,±(2+\sqrt5),\,±(2+\sqrt5),\,±\frac12\right),$$
 * $$\left(±\frac12,\,±\frac12,\,±\frac{3+2\sqrt5}{2},\,±\frac{5+2\sqrt5}{2},\,±\frac12\right),$$
 * $$\left(±\frac{2+\sqrt5}{2},\,±\frac{2+\sqrt5}{2},\,±\frac{3+2\sqrt5}{2},\,±\frac{3+2\sqrt5}{2},\,±\frac12\right),$$
 * $$\left(0,\,±\frac12,\,±3\frac{1+\sqrt5}{4},\,±\frac{11+5\sqrt5}{4},\,±\frac12\right),$$
 * $$\left(0,\,±\frac{1+\sqrt5}{2},\,±(3+\sqrt5),\,±\frac{3+\sqrt5}{2},\,±\frac12\right),$$
 * $$\left(0,\,±\frac{4+\sqrt5}{2},\,±\frac{7+3\sqrt5}{4},\,±3\frac{3+\sqrt5}{4},\,±\frac12\right),$$
 * $$\left(±\frac12,\,±\frac{1+\sqrt5}{4},\,±\frac{5+3\sqrt5}{2},\,±\frac{3+\sqrt5}{4},\,±\frac12\right),$$
 * $$\left(±\frac12,\,±\frac{1+\sqrt5}{4},\,±(3+\sqrt5),\,±\frac{5+3\sqrt5}{4},\,±\frac12\right),$$
 * $$\left(±\frac12,\,±\frac{1+\sqrt5}{2},\,±\frac{11+5\sqrt5}{4},\,±\frac{5+\sqrt5}{4},\,±\frac12\right),$$
 * $$\left(±\frac12,\,±\frac{5+\sqrt5}{4},\,±(2+\sqrt5),\,±3\frac{3+\sqrt5}{4},\,±\frac12\right),$$
 * $$\left(±\frac12,\,±\frac{2+\sqrt5}{2},\,±\frac{5+2\sqrt5}{2},\,±\frac{4+\sqrt5}{2},\,±\frac12\right),$$
 * $$\left(±\frac{1+\sqrt5}{4},\,±1,\,±\frac{2+\sqrt5}{2},\,±\frac{11+5\sqrt5}{4},\,±\frac12\right),$$
 * $$\left(±\frac{1+\sqrt5}{4},\,±\frac{3+\sqrt5}{2},\,±\frac{3+2\sqrt5}{2},\,±3\frac{3+\sqrt5}{4},\,±\frac12\right),$$
 * $$\left(±\frac{1+\sqrt5}{4},\,±\frac{5+3\sqrt5}{4},\,±(2+\sqrt5),\,±\frac{4+\sqrt5}{2},\,±\frac12\right),$$
 * $$\left(±1,\,±\frac{3+\sqrt5}{4},\,±\frac{5+2\sqrt5}{2},\,±\frac{7+3\sqrt5}{4},\,±\frac12\right),$$
 * $$\left(±\frac{3+\sqrt5}{4},\,±\frac{5+\sqrt5}{4},\,±\frac{2+\sqrt5}{2},\,±(3+\sqrt5),\,±\frac12\right),$$
 * $$\left(±\frac{3+\sqrt5}{4},\,±\frac{5+\sqrt5}{4},\,±\frac{3+2\sqrt5}{2},\,±(2+\sqrt5),\,±\frac12\right),$$
 * $$\left(±\frac{3+\sqrt5}{4},\,±3\frac{1+\sqrt5}{4},\,±\frac{5+2\sqrt5}{2},\,±\frac{3+\sqrt5}{2},\,±\frac12\right),$$
 * $$\left(±\frac{1+\sqrt5}{2},\,±\frac{5+\sqrt5}{4},\,±\frac{5+3\sqrt5}{4},\,±\frac{5+2\sqrt5}{2},\,±\frac12\right),$$
 * $$\left(±\frac{1+\sqrt5}{2},\,±\frac{5+3\sqrt5}{4},\,±\frac{3+2\sqrt5}{2},\,±\frac{7+3\sqrt5}{4},\,±\frac12\right),$$
 * $$\left(±\frac{2+\sqrt5}{2},\,±3\frac{1+\sqrt5}{4},\,±(2+\sqrt5),\,±\frac{5+3\sqrt5}{4},\,±\frac12\right).$$