Inflation rules of square-triangle tilings: from approximants to dodecagonal liquid quasicrystals

Abstract

An inflation rule for square-triangle tilings is presented and its properties described. Its relationship to other previously found inflation rules, used to generate models of dodecagonal quasicrystals, is discussed. The rule is applied to generate a series of approximants of dodecagonal quasicrystal, including the well-known and P4 ₂ /mnm structures. The bigger the unit cell dimensions, the closer the structures of these approximants are to that of the dodecagonal quasicrystal.