Re: [math-fun] Penrose tilings, pharmaceuticals and crankery

Actually, Adam wrote "actually wrong" and gave an counterexample for the case where reflections are allowed. --Dan P.S. I agree the result is likely to be true. And that the proof has the appearance of validity, though I know very little about group representations. I can't help wondering if there is a much simpler geometric proof not requiring heavy machinery, and if the statement might be true in much greater generality.

In particular I think the claim above Goucher said was "obviously wrong" is likely in fact correct, and with a correct proof, albeit you might want to be a bit more careful about exactly what is meant by "group" (rotations only) and exactly what polytopes are allowed (nondegenerate only).