Great prismated demitesseract

The great prismated demitesseract or omnitruncated demitesseract is a convex semi-uniform polychoron that is a variant of the truncated icositetrachoron with demitesseractic symmetry. As such it can be represented by a3b3c *b3d, and has 24 great rhombitetratetrahedra (of three types, forms a3b3c, a3b3c, and c3b3d) and 24 cuboids (type a c d) as cells, with 4 edge lengths.

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


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