Quasicrystals: A matter of definition

TL;DR

This paper challenges the traditional definition of quasicrystals, proposing that structures without forbidden symmetries should also be considered quasicrystals, broadening the scope of what is recognized as such.

Contribution

It introduces a revised definition of quasicrystals that includes structures lacking forbidden symmetries, expanding the understanding of quasicrystalline matter.

Findings

Traditional definition excludes some quasicrystals.

Structures without forbidden symmetries exhibit quasicrystal properties.

Proposes a more inclusive definition of quasicrystals.

Abstract

It is argued that the prevailing definition of quasicrystals, requiring them to contain an axis of symmetry that is forbidden in periodic crystals, is inadequate. This definition is too restrictive in that it excludes an important and interesting collection of structures that exhibit all the well-known properties of quasicrystals without possessing any forbidden symmetries.