Great rhombitetratetrahedron

The great rhombitetratetrahedron, or gratet, is a convex semi-uniform polyhedron that is a tetrahedral-symmetric variant of the truncated octahedron. It has 2 sets of 4 ditrigons and 6 rectangles as faces. It generally has 3 types of edge lengths, connecting each pair of face types.

It can be generally alternated into a snub tetrahedron.

Vertex coordinates
A great rhombitetratetrahedron with edges of length a, b, and c, where a and c are the rectangle edges and b edges are between the two types of ditrigons, has vertex coordinates given by all permutation and even sign changes of:


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