Prismatorhombated hexacosichoric prism

The prismatorhombated hexacosichoric prism or prixip is a prismatic uniform polyteron that consists of 2 prismatorhombated hexacosichora, 120 truncated dodecahedral prisms, 600 cuboctahedral prisms, 720 square-decagonal duoprisms, and 1200 triangular-square duoprisms. 1 prismatorhombated hexacosichoron, 1 truncated dodecahedral prism, 1 cuboctahedral prism, 2 square-decagonal duoprisms, and 1 triangular-square duoprism join at each vertex. As the name suggests, it is a prism based on the prismatorhombated hexacosichoron, which also makes it a convex segmentoteron.

Vertex coordinates
The vertices of a prismatorhombated hexacosichoric prism of edge length 1 are given by all permutations of the first four coordinates of: Plus all even permutations of the first four coordinates of:
 * $$\left(0,\,±1,\,±\frac{7+3\sqrt5}{2},\,±\frac{7+3\sqrt5}{2},\,±\frac12\right),$$
 * $$\left(±\frac12,\,±\frac12,\,±3\frac{2+\sqrt5}{2},\,±\frac{8+3\sqrt5}{2},\,±\frac12\right),$$
 * $$\left(±\frac12,\,±\frac12,\,±\frac{3+2\sqrt5}{2},\,±\frac{9+4\sqrt5}{2},\,±\frac12\right),$$
 * $$\left(±\frac{2+\sqrt5}{2},\,±\frac{5+2\sqrt5}{2},\,±3\frac{2+\sqrt5}{2},\,±3\frac{2+\sqrt5}{2},\,±\frac12\right),$$
 * $$\left(±\frac{3+\sqrt5}{2},\,±\frac{3+\sqrt5}{2},\,±\frac{5+3\sqrt5}{2},\,±\frac{7+3\sqrt5}{2},\,±\frac12\right),$$
 * $$\left(0,\,±\frac12,\,±\frac{17+9\sqrt5}{4},\,±\frac{5+3\sqrt5}{4},\,±\frac12\right),$$
 * $$\left(0,\,±\frac{5+\sqrt5}{4},\,±\frac{13+7\sqrt5}{4},\,±3\frac{2+\sqrt5}{2},\,±\frac12\right),$$
 * $$\left(0,\,±\frac{2+\sqrt5}{2},\,±\frac{19+7\sqrt5}{4},\,±3\frac{3+\sqrt5}{4},\,±\frac12\right),$$
 * $$\left(0,\,±3\frac{1+\sqrt5}{4},\,±\frac{17+7\sqrt5}{4},\,±\frac{5+2\sqrt5}{2},\,±\frac12\right),$$
 * $$\left(±\frac12,\,±(3+\sqrt5),\,±\frac{11+5\sqrt5}{4},\,±\frac{13+5\sqrt5}{4},\,±\frac12\right),$$
 * $$\left(±\frac12,\,±\frac{3+\sqrt5}{4},\,±\frac{15+7\sqrt5}{4},\,±\frac{5+3\sqrt5}{2},\,±\frac12\right),$$
 * $$\left(±\frac12,\,±\frac{3+\sqrt5}{4},\,±\frac{19+7\sqrt5}{4},\,±(2+\sqrt5),\,±\frac12\right),$$
 * $$\left(±\frac12,\,±\frac{3+\sqrt5}{4},\,±\frac{17+9\sqrt5}{4},\,±\frac{3+\sqrt5}{2},\,±\frac12\right),$$
 * $$\left(±\frac12,\,±\frac{1+\sqrt5}{2},\,±\frac{17+7\sqrt5}{4},\,±\frac{9+5\sqrt5}{4},\,±\frac12\right),$$
 * $$\left(±\frac12,\,±\frac{2+\sqrt5}{2},\,±\frac{9+4\sqrt5}{2},\,±\frac{5+2\sqrt5}{2},\,±\frac12\right),$$
 * $$\left(±\frac12,\,±\frac{3+\sqrt5}{2},\,±\frac{13+7\sqrt5}{4},\,±\frac{13+5\sqrt5}{4},\,±\frac12\right),$$
 * $$\left(±\frac12,\,±\frac{5+3\sqrt5}{4},\,±\frac{15+7\sqrt5}{4},\,±(3+\sqrt5),\,±\frac12\right),$$
 * $$\left(±1,\,±\frac{3+\sqrt5}{4},\,±\frac{9+4\sqrt5}{2},\,±\frac{7+3\sqrt5}{4},\,±\frac12\right),$$
 * $$\left(±1,\,±\frac{2+\sqrt5}{2},\,±\frac{15+7\sqrt5}{4},\,±\frac{11+5\sqrt5}{4},\,±\frac12\right),$$
 * $$\left(±\frac{3+\sqrt5}{4},\,±\frac{9+5\sqrt5}{4},\,±3\frac{2+\sqrt5}{2},\,±(3+\sqrt5),\,±\frac12\right),$$
 * $$\left(±\frac{3+\sqrt5}{4},\,±\frac{1+\sqrt5}{2},\,±\frac{17+9\sqrt5}{4},\,±\frac{2+\sqrt5}{2},\,±\frac12\right),$$
 * $$\left(±\frac{3+\sqrt5}{4},\,±3\frac{1+\sqrt5}{4},\,±\frac{9+4\sqrt5}{2},\,±\frac{3+\sqrt5}{2},\,±\frac12\right),$$
 * $$\left(±\frac{3+\sqrt5}{4},\,±\frac{5+2\sqrt5}{2},\,±\frac{7+3\sqrt5}{2},\,±\frac{13+5\sqrt5}{4},\,±\frac12\right),$$
 * $$\left(±\frac{3+\sqrt5}{4},\,±\frac{7+3\sqrt5}{4},\,±\frac{8+3\sqrt5}{2},\,±(3+\sqrt5),\,±\frac12\right),$$
 * $$\left(±\frac{3+\sqrt5}{4},\,±\frac{5+2\sqrt5}{2},\,±\frac{5+3\sqrt5}{2},\,±\frac{13+5\sqrt5}{4},\,±\frac12\right),$$
 * $$\left(±\frac{1+\sqrt5}{2},\,±\frac{5+\sqrt5}{4},\,±\frac{5+3\sqrt5}{4},\,±\frac{9+4\sqrt5}{2},\,±\frac12\right),$$
 * $$\left(±\frac{1+\sqrt5}{2},\,±3\frac{3+\sqrt5}{4},\,±3\frac{2+\sqrt5}{2},\,±\frac{13+5\sqrt5}{4},\,±\frac12\right),$$
 * $$\left(±\frac{1+\sqrt5}{2},\,±(2+\sqrt5),\,±\frac{7+3\sqrt5}{2},\,±(3+\sqrt5),\,±\frac12\right),$$
 * $$\left(±\frac{5+\sqrt5}{4},\,±\frac{3+\sqrt5}{2},\,±\frac{8+3\sqrt5}{2},\,±\frac{11+5\sqrt5}{4},\,±\frac12\right),$$
 * $$\left(±\frac{2+\sqrt5}{2},\,±\frac{9+5\sqrt5}{4},\,±\frac{5+3\sqrt5}{2},\,±\frac{11+5\sqrt5}{4},\,±\frac12\right),$$
 * $$\left(±\frac{2+\sqrt5}{2},\,±\frac{3+\sqrt5}{2},\,±\frac{5+3\sqrt5}{4},\,±\frac{19+7\sqrt5}{4},\,±\frac12\right),$$
 * $$\left(±\frac{2+\sqrt5}{2},\,±\frac{3+2\sqrt5}{2},\,±\frac{8+3\sqrt5}{2},\,±\frac{5+2\sqrt5}{2},\,±\frac12\right),$$
 * $$\left(±3\frac{1+\sqrt5}{4},\,±(2+\sqrt5),\,±3\frac{2+\sqrt5}{2},\,±\frac{11+5\sqrt5}{4},\,±\frac12\right),$$
 * $$\left(±\frac{3+\sqrt5}{2},\,±\frac{5+3\sqrt5}{4},\,±\frac{8+3\sqrt5}{2},\,±\frac{9+5\sqrt5}{4},\,±\frac12\right),$$
 * $$\left(±\frac{3+\sqrt5}{2},\,±\frac{5+2\sqrt5}{2},\,±\frac{7+3\sqrt5}{4},\,±\frac{17+7\sqrt5}{4},\,±\frac12\right),$$
 * $$\left(±\frac{3+\sqrt5}{2},\,±\frac{3+2\sqrt5}{2},\,±\frac{15+7\sqrt5}{4},\,±3\frac{3+\sqrt5}{4},\,±\frac12\right),$$
 * $$\left(±\frac{5+3\sqrt5}{4},\,±\frac{5+2\sqrt5}{2},\,±(2+\sqrt5),\,±\frac{15+7\sqrt5}{4},\,±\frac12\right),$$
 * $$\left(±\frac{5+3\sqrt5}{4},\,±\frac{7+3\sqrt5}{4},\,±3\frac{2+\sqrt5}{2},\,±\frac{5+3\sqrt5}{2},\,±\frac12\right),$$
 * $$\left(±\frac{5+3\sqrt5}{4},\,±\frac{3+2\sqrt5}{2},\,±\frac{7+3\sqrt5}{2},\,±\frac{9+5\sqrt5}{4},\,±\frac12\right),$$
 * $$\left(±\frac{7+3\sqrt5}{4},\,±\frac{3+2\sqrt5}{2},\,±\frac{13+7\sqrt5}{4},\,±(2+\sqrt5),\,±\frac12\right).$$