Truncated hexacosichoric prism

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

Vertex coordinates
The vertices of a truncated hexacosichoron of edge length 1 are given by all even permutations of the first four coordinates of:
 * $$\left(0,\,±\frac12,\,±\frac{1+\sqrt5}{4},\,±\frac{7+5\sqrt5}{4},\,±\frac12\right),$$
 * $$\left(0,\,±\frac12,\,±\frac{3+3\sqrt5}{4},\,±\frac{9+3\sqrt5}{4},\,±\frac12\right),$$
 * $$\left(0,\,±1,\,±\frac{1+\sqrt5}{2},\,±(2+\sqrt5),\,±\frac12\right),$$
 * $$\left(0,\,±\frac{5+\sqrt5}{4},\,±\frac{5+3\sqrt5}{4},\,±\frac{4+\sqrt5}{2},\,±\frac12\right),$$
 * $$\left(0,\,±\frac{2+\sqrt5}{2},\,±\frac{7+3\sqrt5}{4},\,±\frac{7+\sqrt5}{4},\,±\frac12\right),$$
 * $$\left(±\frac12,\,±1,\,±\frac{5+3\sqrt5}{4},\,±\frac{7+3\sqrt5}{4},\,±\frac12\right),$$
 * $$\left(±\frac12,\,±\frac{1+\sqrt5}{2},\,±\frac{9+3\sqrt5}{4},\,±\frac{5+\sqrt5}{4},\,±\frac12\right),$$
 * $$\left(±\frac{1+\sqrt5}{4},\,±1,\,±\frac{2+\sqrt5}{2},\,±\frac{9+3\sqrt5}{4},\,±\frac12\right),$$
 * $$\left(±\frac{1+\sqrt5}{4},\,±\frac{5+\sqrt5}{4},\,±\frac{3+3\sqrt5}{4},\,±\frac{7+3\sqrt5}{4},\,±\frac12\right),$$
 * $$\left(±\frac{1+\sqrt5}{2},\,±\frac{2+\sqrt5}{2},\,±\frac{3+3\sqrt5}{4},\,±\frac{5+3\sqrt5}{4},\,±\frac12\right).$$