Bindi, Luca Dipartimento di Scienze della Terra, Università di Firenze, Firenze, Italy.
Steinhardt, Paul J. Princeton Center for Theoretical Science and Department of Physics, Princeton University, Princeton, New Jersey.
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The regularly repeating atomic arrangement in crystals is called periodic. The hexagons in a honeycomb lattice (Fig. 1a) or the square tiles in bathroom tiling are examples of periodic tessellations. According to the laws of mathematics discovered in the nineteenth century, periodicity can only occur for certain rotational symmetries, such that one-, two-, three-, four-, and sixfold symmetry are allowed, but crystals or periodic tilings with five-, seven-, eight-, or higher-fold symmetry axes are strictly forbidden. About thirty years ago, however, a new kind of material that violates these rules was hypothesized and dubbed quasicrystals (short for quasiperiodic crystals), and, independently, a synthetic example was discovered in the laboratory. Since then, over a hundred different quasicrystals have been made in the laboratory using highly controlled synthetic methods.
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