I immediately tried to construct my favorite obscure polyhedron (the rhombic dodecahedron) and found I simply could not take the dual of the cuboctahedron! :P
That aside, this is a really fantastic little toy here - I'd never really understood the relationships between all these shapes before, or exactly what some of these operations were, geometrically speaking.
> favorite obscure polyhedron (the rhombic dodecahedron)
Obscure? Come on! The rhombic dodecahedron is the Voronoi cell of the FCC lattice, making it (arguably) the most natural 3-dimensional analog of the hexagon. It shows up all over the place!
It's "obscure" to me (and also my favorite) because I had never even heard of it before I tried to find out what the most natural 3-dimensional analog of the hexagon was. :)
That aside, this is a really fantastic little toy here - I'd never really understood the relationships between all these shapes before, or exactly what some of these operations were, geometrically speaking.