Prismatorhombated demitesseract

The prismatorhombated demitesseract is a convex semi-uniform polychoron that is a variant of the rectified icositetrachoron with demitesseractic symmetry. As such it can be represented by x3o3y *b3z, and has 24 rhombitetratetrahedra (of three types, forms x3o3y, x3o3z, and y3o3z) and 24 cuboids (type x y z) as cells, with 3 edge lengths.

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


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