[math-fun] Non-standard "polyhedra" ...

Forgive me if this is obvious and well-known. Because of Euler we know that for polyhedra without holes we have V+F=E+2. As a result we can't have a polyhedron made entirely of hexagons, and need at least 12 pentagons or an equivalent set of shapes. Etc. But things change if we allow intersecting faces. Clearly we have a lot of scope for variations, but we can always retain limits to make things reasonable. But ... Can we make a "polyhedron" consisting only of hexagonal "faces"? Thanks Colin -- Every mathematical proof is a one liner if you start far enough on the left -- Anon