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:
 * $$\left(±\frac{\sqrt2}{2},\,±\frac{\sqrt2}{2},\,±\frac{\sqrt2}{2},\,±\frac{\sqrt2}{2},\,0\right).$$

Representations
A rectified penteract has the following Coxeter diagrams:


 * o4x3o3o3o (full symmmetry)
 * x3o3x *b3o3o (D5 symmetry)
 * s4x3o3o3o (D5 symmetry, as alternated faceting)
 * oqo4xox3ooo3ooo&#xt (B4 axial, rectified tesseract-first)
 * xxooo3oxxoo3ooxxo3oooxx&#xt (A4 axial, pentachoron-first)

Related polytopes
The rectified penteract is the colonel of a regiment of 11 members, where 7 have full symmetry and the other 4 have half symmetry.