I have a polyhedra-like graph I want to make the polyhedra (or polyhedra-like surface) of.
It looks to be a truncated octahedron, except there's extra vertices in the middle of every edge and face. The face midpoints are connected to the edge midpoints, and the edge midpoints are connected to the vertices of the original edge.
I'd like a function to do this connected-midpoints operation on any generic polyhedra I pass in.
I note that it's not a "proper" polyhedra, so if Mathematica just won't let it be constructed, that's a fine answer too.