This has the symmetry group which consists of just four operators: identity, and rotation around the three axes. One of my very favorite groups – none is more elegant.
I'm moving this design to Shapeways because I can offer it there in so many materials and finishes. Their polished bronze and precious metals are amazing, and the plastics are cute and cheap.
Accordingly I'm selling off my steel stock: it's a good price but when they're gone they're gone.