Great rhombated demitesseract

The great rhombated demitesseract or runcicantic tesseract is a convex semi-uniform polychoron that is a variant of the tesseractihexadecachoron with demitesseractic symmetry. As such it can be represented by x3y3o *b3z, and has 16 truncated tetrahedra (of two types, forms x3y3o and z3y3o) and 8 great rhombitetrahedra (type x3y3z) as cells, with 3 edge lengths.

Vertex coordinates
A great rhombated demitesseract with edge lengths a, b, and c has vertices given by all permutations and even sign changes of:


 * $$\left((a+2b+c)\frac{\sqrt2}{4},\,(a+b)\frac{\sqrt2}{4},\,a\frac{\sqrt2}{4},\,a\frac{\sqrt2}{4}\right).$$

Alternative coordinates in a different orientation can be given by all even sign changes and permutations of:


 * $$\left((a+2b+c)\frac{\sqrt2}{4},\,(a+2b+c)\frac{\sqrt2}{4},\,(a+c)\frac{\sqrt2}{4},\,(a-c)\frac{\sqrt2}{4}\right).$$