Prismatotruncatodemipenteract

The prismatotruncatodemipenteract, or pithin, also called the stericantic 5-cube, is a convex uniform polyteron. It consists of 40 truncated tetrahedral prisms, 16 small rhombated pentachora, 10 truncated hexadecachora, and 16 prismatorhombated pentachora. 1 small rhombated pentachoron, 1 truncated hexadecachora, 2 prismatorhombated pentachora, and 2 truncated tetrahedral prisms join at each vertex. It can be formed from an alternated faceting of the cellirhombipenteractitriacontaditeron.

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

Representations
A prismatorhombatodemipenteract has the following Coxeter diagrams:


 * x3x3o *b3o3x (full symmetry)
 * s4o3x3o3x (as alternated faceting)
 * oox(uo)(ox)xx-3-xux(xu)(xu)xo-3-oox(xo)(oo)ox-3-xxx(ou)(dx)ux-&#xt (A4 axial, small rhombated pentachoron-first)

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