Prismatotruncatodemihexeract

The prismatotruncatodemihexeract or pithax, also called the stericantic 6-cube or runcitruncated 6-demicube, is a convex uniform polypeton. It consists of 12 prismatorhombated demipenteracts, 32 small birhombated dodecatera, 32 prismatotruncated hexatera, and 160 triangular-truncated tetrahedral duoprisms. 2 prismatorhombated demipenteracts, 1 small birhombated hexateron, 2 prismatotruncated hexatera, and 2 triangular-truncated tetrahedral duoprisms join at each vertex. As the name suggests, it is the runcitruncation of the demihexeract.

Coordinates
The vertex coordinates of a prismatotruncatodemihexeract, centered at the origin and with unit edge length, are given by all permutations and even sign changes of:
 * $$\left(\frac{5\sqrt8}{8},\,\frac{5\sqrt8}{8},\,\frac{3\sqrt8}{8},\,\frac{3\sqrt8}{8},\,\frac{\sqrt8}{8},\,\frac{\sqrt8}{8}\right).$$

Representations
A prismatotruncatodemihexeract has the following Coxeter diagrams:
 * x3x3o *b3o3x3o (full symmetry)
 * s4o3x3o3x3o (as alternated small birhombated hexacontatetrapeton)