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Pentagonal and Icosahedral Order in Rapidly Cooled Metals

The discovery of an alloy of aluminum and manganese with sharp Bragg diffraction spots and an icosahedral point group symmetry was announced last year. The icosahedral symmetry appears to be an intrinsic property of the material and not an artifact of twinning. There are remarkable similarities between the observed diffraction patterns and aperiodic tesselations of space called Penrose tiles. The relation between the experiments and Penrose tiles, as well as phenomenological descriptions of the icosahedral aluminum-manganese alloy as a superposition of incommensurate density waves, are reviewed. Other types of exotic crystallography are also discussed.