TOPOLOGICAL CONSTRAINTS FOR QUASICRYSTALS

Abstract

Topological constraints necessary for the existence of icosahedral quasicrystals having continuous phasons are found. As a result of application of these constraints a model of a new type for icosahedral quasicrystals is constructed. The “atomic surfaces” in R6 in this model are free of discontinuities, i.e. the displacements of atoms are continuous as functions of a phason shift. The positions of atoms in the physical space R3 from 60 interpenetrating rhombohedral lattices. The model exhibits diffraction properties of an ideal quasiperiodic structure and has perfect icosahedral symmetry.