Bravais classes for incommensurate crystal phases

Abstract

A full classification is given of the Bravais classes of lattices of symmetry groups of incommensurate crystal phases with an internal (additional) dimensionality d lower than four. These Bravais classes form the basis for the derivation of superspace groups needed for the symmetry classification of incommensurate crystal phases. By means of examples it is indicated how the information contained in the various tables can be extracted and used, for example, for the derivation of superspace groups.