Scale equivalence of quasicrystallographic space groups

Abstract

The space-group classification of ordered structures has been extended to quasicrystals by formulating the problem in wave-vector space. We list the space groups belonging to the icosahedral point groups Y and ${Y}_{h}$ for the three icosahedral lattices of wave vectors, and show that taking into account the scaling properties of quasicrystal lattices is crucial for a correct enumeration.