Cellitruncatodemihexeract

The cellitruncatodemihexeract or cathix, also called the penticantic 6-cube or steritruncated 6-demicube, is a convex uniform polypeton. It consists of 12 truncated demipenteracts, 32 small prismated hexatera, 32 celliprismated hexatera, 160 triangular-truncated tetrahedral duoprisms, and 60 truncated hexadecachoric prisms. 1 truncated demipenteract, 1 small prismated hexateron, 2 celliprismated hexatera, 3 triangular-truncated tetrahedral duoprisms, and 3 truncated hexadecachoric prisms join at each vertex. As the name suggests, it is the steritruncation of the demihexeract.

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

Representations
A cellitruncatodemihexeract has the following Coxeter diagrams:
 * x3x3o *b3o3o3x (full symmetry)
 * s4o3x3o3o3x (as alternated teriprismated hexacontatetrapeton)