Geometry and symmetry of multilattices

Abstract

Abstract We extend to multilattices some of Ericksen's ideas about invariance of continuum constitutive equations for a solid that can be regarded as a simple crystalline lattice from the molecular point of view. In particular we analyze properties of lattice groups of multilattices and of their fixed sets, and prove that a natural classification of such groups provides a finer description of symmetry than the classes of space groups of classical crystallography. We also provide a simple criterion to see whether or not the descriptors of a multilattice correspond to its maximal translational invariance.