Small rhombidemipenteract

The small rhombidemipenteract, or sirhin, also called the runcic 5-cube, is a convex uniform polyteron. It consists of 16 rectified pentachora, 16 small rhombated pentachora, and 10 rectified tesseracts. One rectified pentachoron, 2 rectified tesseracts, and 3 small rhombated pentachora join at each vertex. It can be formed from an alternated faceting of the small prismated penteract, or as a birectification of the demipenteract.

Vertex coordinates
The vertices of a small rhombidemipenteract of edge length 1 are given by all permutations and even sign changes of:
 * $$\left(\frac{3\sqrt2}{4},\,\frac{3\sqrt2}{4},\,\frac{\sqrt2}{4},\,\frac{\sqrt2}{4},\,\frac{\sqrt2}{4}\right).$$

Representations
A small rhombidemipenteract has the following Coxeter diagrams:


 * x3o3o *b3x3o (full symmetry)
 * s4o3o3x3o (as alternated faceting)
 * xxoo3oxxo3ooxx *b3xoox&#xt (D4 axial, rectified tesseract-first)

Related polytopes
The regiment of the small rhombidemipenteract includes a total of 37 members plus one fissary member.