Hexacosihecatonicosachoric prism

The hexacosihecatonicosachoric prism or xhip is a prismatic uniform polyteron that consists of 2 truncated hexacosichora, 120 truncated icosahedral prisms, and 600 truncated tetrahedral prisms. 1 hexacosihecatonicosachoron, 2 truncated icosahedral prisms, and 2 truncated tetrahedral prisms join at each vertex. As the name suggests, it is a prism based on the hexacosihecatonicosachoron, which also makes it a convex segmentoteron.

Vertex coordinates
Coordinates for the vertices of a hexacosihecatonicosachoric prism of edge length 1 are given by all permutations of the first four coordinates of: together with all even permutations of the first four coordinates of:
 * $$\left(0,\,0,\,±(1+\sqrt5),\,±\frac{7+3\sqrt5}{2},\,±\frac12\right),$$
 * $$\left(±\frac{5+\sqrt5}{4},\,±\frac{5+\sqrt5}{4},\,±\frac{9+5\sqrt5}{4},\,±\frac{9+5\sqrt5}{4},\,±\frac12\right),$$
 * $$\left(0,\,±\frac12,\,±\frac{13+5\sqrt5}{4},\,±\frac{7+5\sqrt5}{4},\,±\frac12\right),$$
 * $$\left(0,\,±\frac12,\,±3\frac{1+\sqrt5}{4},\,±\frac{13+7\sqrt5}{4},\,±\frac12\right),$$
 * $$\left(0,\,±\frac{1+\sqrt5}{4},\,±5\frac{3+\sqrt5}{4},\,±\frac{3+2\sqrt5}{2},\,±\frac12\right),$$
 * $$\left(0,\,±3\frac{3+\sqrt5}{4},\,±\frac{5+2\sqrt5}{2},\,±\frac{11+3\sqrt5}{4},\,±\frac12\right),$$
 * $$\left(±\frac12,\,±\frac{1+\sqrt5}{2},\,±\frac{13+7\sqrt5}{4},\,±\frac{5+\sqrt5}{4},\,±\frac12\right),$$
 * $$\left(±\frac12,\,±\frac{1+\sqrt5}{2},\,±5\frac{3+\sqrt5}{4},\,±\frac{7+3\sqrt5}{4},\,±\frac12\right),$$
 * $$\left(±\frac12,\,±1,\,±\frac{11+5\sqrt5}{4},\,±\frac{9+5\sqrt5}{4},\,±\frac12\right),$$
 * $$\left(±\frac12,\,±\frac{3+\sqrt5}{2},\,±\frac{11+5\sqrt5}{4},\,±\frac{11+3\sqrt5}{4},\,±\frac12\right),$$
 * $$\left(±\frac{1+\sqrt5}{4},\,±1,\,±\frac{2+\sqrt5}{2},\,±\frac{13+7\sqrt5}{4},\,±\frac12\right),$$
 * $$\left(±\frac{1+\sqrt5}{4},\,±\frac{7+3\sqrt5}{4},\,±\frac{9+5\sqrt5}{4},\,±\frac{11+3\sqrt5}{4},\,±\frac12\right),$$
 * $$\left(±\frac{1+\sqrt5}{2},\,±\frac{3+2\sqrt5}{2},\,±\frac{9+5\sqrt5}{4},\,±3\frac{3+\sqrt5}{4},\,±\frac12\right),$$
 * $$\left(±\frac{1+\sqrt5}{2},\,±\frac{7+3\sqrt5}{4},\,±\frac{7+5\sqrt5}{4},\,±\frac{5+2\sqrt5}{2},\,±\frac12\right),$$
 * $$\left(±1,\,±\frac{1+\sqrt5}{2},\,±\frac{7+3\sqrt5}{2},\,±\frac{3+\sqrt5}{2},\,±\frac12\right),$$
 * $$\left(±1,\,±\frac{2+\sqrt5}{2},\,±\frac{13+5\sqrt5}{4},\,±3\frac{3+\sqrt5}{4},\,±\frac12\right),$$
 * $$\left(±1,\,±\frac{5+\sqrt5}{4},\,±\frac{11+5\sqrt5}{4},\,±\frac{5+2\sqrt5}{2},\,±\frac12\right),$$
 * $$\left(±\frac{2+\sqrt5}{2},\,±(1+\sqrt5),\,±\frac{11+5\sqrt5}{4},\,±\frac{7+3\sqrt5}{4},\,±\frac12\right),$$
 * $$\left(±\frac{2+\sqrt5}{2},\,±\frac{3+\sqrt5}{2},\,±\frac{7+5\sqrt5}{4},\,±\frac{9+5\sqrt5}{4},\,±\frac12\right),$$
 * $$\left(±3\frac{1+\sqrt5}{4},\,±\frac{3+\sqrt5}{2},\,±\frac{3+2\sqrt5}{2},\,±\frac{11+5\sqrt5}{4},\,±\frac12\right),$$
 * $$\left(±\frac{5+\sqrt5}{4},\,±\frac{2+\sqrt5}{2},\,±5\frac{3+\sqrt5}{4},\,±\frac{3+\sqrt5}{2},\,±\frac12\right),$$
 * $$\left(±\frac{5+\sqrt5}{4},\,±3\frac{1+\sqrt5}{4},\,±\frac{13+5\sqrt5}{4},\,±\frac{7+3\sqrt5}{4},\,±\frac12\right).$$