Great prismatodemipenteract

The great prismatodemipenteract, or giphin, also called the steriruncicantic 5-cube, is a convex uniform polyteron. It consists of 40 truncated tetrahedral prisms, 16 great rhombated pentachora, 10 tesseractihexadecachora, and 16 great prismatodecachora. 2 great prismatodecachora, 1 great rhombated pentachoron, 1 tesseractihexadecachoron, and 1 trunctaed tetrahedral prism join at each vertex. It can be formed from an alternated faceting of the celligreatorhombated triacontaditeron.

Vertex coordinates
The vertices of a great prismatodemipenteract of edge length 1 are given by all permutations and even sign changes of:
 * $$\left(\frac{7\sqrt2}{4},\,\frac{5\sqrt2}{4},\,\frac{3\sqrt2}{4},\,\frac{\sqrt2}{4},\,\frac{\sqrt2}{4}\right).$$

Representations
A great prismatodemipenteract has the following Coxeter diagrams:


 * x3x3o *b3x3x (full symmetry)
 * s4o3x3x3x (as alternated faceting)