Small rhombated penteract

The small rhombated penteract, or sirn, also called the cantellated 5-cube, is a convex uniform polyteron. It consists of 80 tetrahedral prisms, 32 rectified pentachora, and 10 small rhombated tesseracts. One rectified pentachoron, 2 tetrahedral prisms, and 3 small rhombated tesseracts join at each vertex. As the name suggests, it is the cantellation of the penteract.

The small rhombated penteract contains the vertices of a truncated tesseractic prism and octagonal-truncated cubic duoprism.

Vertex coordinates
The vertices of a small rhombated penteract of edge length 1 are given by all permutations of:
 * $$\left(±\frac{1+\sqrt2}{2},\,±\frac{1+\sqrt2}{2},\,±\frac{1+\sqrt2}{2},\,±\frac12,\,±\frac12\right).$$

Representations
A small rhombated penteract has the following Coxeter diagrams:


 * x4o3x3o3o (full symmetry)
 * xxxx4oxxo3xoox3oooo&#xt (BC4 axial, small rhombated tesseract-first)
 * oxo4wxx xoo3oxo4xxw&#zx (BC3×BC2 symmetry)

Related polytopes
The small rhombated penteract is the colonel of a regiment that includes 15 uniform members.