Quasicrystals and Aperiodic Tilings

Abstract

Two of the proposed explanations of quasicrystal structure are discussed. The quasiperiodic crystal and random tiling models share a common basis in the quasiperiodic tilings that the author presents. The third model, the icosahedral glass, is not included due to space limitations. She discusses only the two-dimensional (d=2) versions of the models, both for computational simplicity and because the resulting patterns are more easily visualized. She also limits her discussion to fivefold symmetric quasicrystals, although other symmetries have been studied using these techniques