Symmetry and symmetry breaking of quasicrystals and their applications

Abstract

This paper gives a detailed review on symmetry and symmetry breaking of quasicrystals. The symmetry groups of solid and soft-matter quasicrystals observed so far are summarized and the symmetry breakings of quasicrystals are systematically discussed. The present review connects several branches of mathematics and physics and related applications in science and technology are also discussed.