Prior to the discovery of quasicrystals, it was thought that five-fold crystal symmetry was impossible, because there are no space-filling periodic tilings of this kind. The best known examples of quasicrystals resemble Penrose tilings, which use repeated copies of two different rhombi to cover an infinite plane in intricate, interlocking patterns. In fact, some quasicrystals can be sliced in such a way that the atoms on the surface follow the exact pattern of the Penrose tiling.
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