Quasicrystals

We review the structure of quasicrystals and their electronic spectra, lattice excitation spectra, physical properties, and applications. The aperiodic filling of space according to certain rules with several structural units or overlapping atomic clusters is discussed. Perfect tiling, random tiling, and icosahedral glass models, as well as phason strain are considered. The effect that the aperiodic long-range order and local atomic structure have on electron and thermal transport and on the optical, magnetic, and other properties is examined. (reviews of topical problems)