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Quasicrystals. Crystals are surely the oldest known of the broken-symmetry phases of matter, and remain the most beautiful illustrations. It's amazing that in the past few years, we've uncovered an entirely new class of crystals. Shown here is a photograph of a quasicrystalline metallic alloy, with icosahedral symmetry. Notice the five-pointed stars: our old notions of crystals had to be completely revised to include this type of symmetry.
J. H. Lang, M. Audier, B. Dubost, and P. Sainfort, J. of Crystal Growth 83, 456 (1987).
Image courtesy: Drs. Marc Audier, James P. Sethna, Cornell University.