A bizarre consequence of the Crystallography Restriction is that one can't have a wallpaper pattern with with fivefold rotational symmetry but one can have 2-, 3-, 4-, and 6-fold rotational symmetry. It's tricky to explain "fivefold rotational symmetry" concisely and precisely, but I just tried this example out on a friend of mine, and I must say his reaction was fairly enjoyable. He found the result unbelievable.
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