Rectified hexateron

The rectified hexateron, or rix, also called the rectified 5-simplex, is a convex uniform polyteron. It consists of 6 regular pentachora and 6 rectified pentachora. Two pentachora and 4 rectified pentachora join at each tetrahedral prismatic vertex. As the name suggests, it is the rectification of the hexateron.

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


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

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


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