Rectified pentachoron

The rectified pentachoron, or rap, also commonly called the rectified 5-cell, is a convex uniform polychoron that consists of 5 regular tetrahedra and 5 regular octahedra. Two tetrahedra and three octahedra join at each triangular prismatic vertex. It is the vertex figure of the demipenteract.

Vertex coordinates
The vertices of a rectified pentachoron of edge length 1 are given by:


 * (–3$\sqrt{15}$/20, –$\sqrt{5}$/4, 0, 0),
 * (–3$\sqrt{10}$/20, $\sqrt{6}$/12, –$\sqrt{10}$/3, 0),
 * (–3$\sqrt{6}$/20, $\sqrt{3}$/12, $\sqrt{10}$/6, ±1/2),
 * ($\sqrt{6}$/10, $\sqrt{3}$/6, $\sqrt{10}$/3, 0),
 * ($\sqrt{6}$/10, –$\sqrt{3}$/6, –$\sqrt{10}$/3, 0),
 * ($\sqrt{6}$/10, $\sqrt{3}$/6, –$\sqrt{10}$/6, ±1/2),
 * ($\sqrt{6}$/10, –$\sqrt{3}$/6, $\sqrt{10}$/6, ±1/2).

Much simpler coordinates can be given in five dimensions, as all permutations of:


 * ($\sqrt{6}$/2, $\sqrt{3}$/2, 0, 0, 0).