Great rhombated hexadecachoron

The great rhombated hexadecachoron is a convex semi-uniform polychoron that is a variant of the truncated icositetrachoron with tesseractic symmetry. As such it can be represented by o4z3y3x, and has 8 truncated octahedra of form o4z3y, 16 great rhombitetratetrahedra of type x3y3z, and 24 square prisms of type x z4o as cells, with 3 edge lengths.

Vertex coordinates
A great rhombated hexadecachoron with edge lengths a and b has vertices given by all permutations of:


 * $$\left(±(a+b+c)\frac{\sqrt2}{2},\,±(b+c)\frac{\sqrt2}{2},\,±c\frac{\sqrt2}{2},\,0\right).$$