Lattice Color Groups of Quasicrystals

TL;DR

This paper introduces lattice color groups as a tool to analyze the symmetry and partitioning of ordered point sets in both periodic and quasiperiodic crystals, with applications in magnetic and superlattice structures.

Contribution

It presents the concept of lattice color groups and demonstrates their use in understanding symmetry-related partitions in quasicrystals and related materials.

Findings

Lattice color groups effectively classify symmetry partitions.

Applications include magnetic structures and superlattice ordering.

Provides a new framework for analyzing quasiperiodic symmetries.

Abstract

Lattice color groups are introduced and used to study the partitioning of a periodically- or quasiperiodically-ordered set of points into N symmetry-related subsets. Applications range from magnetic structure to superlattice ordering in periodic and quasiperiodic crystals.