Rectified penteract

The rectified penteract, or rin, also called the rectified 5-cube, is a convex uniform polyteron. It consists of 10 rectified tesseracts and 32 pentachora. Two pentachora and 4 rectified tesseracts join at each tetrahedral prismatic vertex. As the name suggests, it is the rectification of the penteract.

Vertex coordinates
The vertices of a rectified penteract of edge length 1 are given by all permutations of:
 * (±$\sqrt{2}$/2, ±$\sqrt{2}$/2, ±$\sqrt{2}$/2, ±$\sqrt{5}$/2, 0).