Rhombitetratetrahedron

The rhombitetratetrahedron, or ratet, is a convex semi-unifrom polyhedron that is a tetrahedral-symmetric variant of the cuboctahedron. It has 2 sets of 4 triangles of generally different sizes, with 6 rectangles connecting them. Half of the edges are of each size.

A rhombitetratetrahedron is the vertex figure of one uniform polychoron, the grand ditetrahedronary hexacosidishecatonicosachoron.

Coordinates
A rhombitetratetrahedron with edge lengths a and b has vertices given by all permutations and even sign changes of:


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