Small rhombated demitesseract

The small rhombated demitesseract or runcic tesseract is a convex semi-uniform polychoron that is a variant of the rectified tesseract with demitesseractic symmetry. As such it can be represented by x3o3o *b3y, and has 16 tetrahedra (of two types, sizes x and y) and 8 rhombitetrahedra (type x3o3y) as cells, with two edge lengths.

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


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

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


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