Prismatorhombidemipenteract

The prismatorhombidemipenteract, or pirhin, also called the steriruncic 5-cube, is a convex uniform polyteron. It consists of 16 truncated pentachora, 40 tetrahedral prisms, 10 rectified tesseracts, and 16 prismatorhombated pentachora. 1 rectified tesseract, 1 truncated pentachoron, 1 tetrahedral prism, and 3 prismatorhombated pentachora join at each vertex. It can be formed from an alternated faceting of the celliprismated penteract.

Vertex coordinates
The vertices of a prismatorhombidemipenteract of edge length 1 are given by all permutations and even sign changes of:
 * $$\left(\frac{5\sqrt2}{4},\,\frac{3\sqrt2}{4},\,\frac{\sqrt2}{4},\,\frac{\sqrt2}{4},\,\frac{\sqrt2}{4}\right).$$

Representations
A prismatorhombated demipenteract has the following Coxeter diagrams:


 * x3o3o *b3x3x (full symmetry)
 * s4o3o3x3x (as alternated faceting)
 * oooxxx3ooxxoo3xxxooo *b3xuxxux&#xt (D4 axial, rectified tesseract-first)

Related polytopes
The prismatorhombidemipenteract is the colonel of a regiment of 7 members.