Aperiodic Crystal Structures: Quasicrystals

Abstract

It is remarkable that while the Platonic solids reflect 5-fold symmetry in both the icosahedra and the dodecahedron, crystal structures did not represent this symmetry until around 1983 when quasicrystals were discovered. This chapter presents a short overview of quasicrystals and 5-fold symmetric structures which have been described over the past three decades. Their relationship to the golden mean or the divine proportion is also briefly discussed. The concept of aperiodic or quasicrystals versus periodic or regular crystals is also described.