Hexacosichoric prism

The hexacosichoric prism or exip is a prismatic uniform polyteron that consists of 2 hexacosichora and 600 tetrahedral prisms. 1 hexacosichoron and 20 tetrahedral prisms join at each vertex. As the name suggests, it is a prism based on the hexacosichoron, which also makes it a convex segmentoteron.

Vertex coordinates
The vertices of a hexacosichoric prism of edge length 1 are given by all permutations and sign changes of the first four coordinates of: together with all the even permutations of the first four coordinates of:
 * (±\frac{1+\sqrt5}{2},\,0,\,0,\,0,\,±\frac12\right),
 * $$\left(±\frac{1+\sqrt5}{4},\,±\frac{1+\sqrt5]{4},\,±\frac{1+\sqrt5}{4},\,±\frac{1+\sqrt5}{4},\,±\frac12\right),$$
 * $$\left(±\frac{3+\sqrt5}{4},\,±\frac{1+\sqrt5}{4},\,±\frac12,\,0,\,±\frac12\right).$$