Forbidden Fivefold Symmetry May Indicate Quasicrystal Phase

You can’t tile a bathroom floor with regular pentagons. The crystallographic equivalent of this mundane truth is the inviolate classical rule that no crystal structure—in two or three dimensions—can possess fivefold rotational symmetry. It was with complete surprise, therefore, that Dan Shechtman and his colleagues recently discovered a fivefold symmetric point diffraction pattern for micron‐size grains of metallic alloy prepared by rapid cooling in their National Bureau of Standards laboratory.

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