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:


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