 So if we define a polyhedron as “normal” if it has no holes or tunnels in it, we can restrict the original conjecture to “normal” polyhedra and avoid this refutation. The trouble with this method is that it reduces the content of the original conjecture, and an empty tautology threatens—“For all Eulerian polyhedra (polyhedra for which \(V - E + F = 2\)V – E + F = 2), V – E + F = 2\(V - E + F = 2\)”. More particularly, a blanket exclusion of polyhedra with holes or tunnels rules out some polyhedra for which \(V - E + F = 2\), despite the presence of a hole—a cube with a square hole drilled through it and two ring-shaped faces being an example – the formula V – E + F = 2 holds good. This suggests a deeper problem than finding the domain of validity of the original conjecture—finding a general relationship between V, E and F for all polyhedra whatsoever.