Classifications of space groups, point groups and lattices

Abstract

Part 8 provides the theoretical background to the data in the tables and diagrams of Volume A. In Chapter 8.2, the different classifications of crystallographic objects are dealt with. The infinite number of three-dimensional space groups is partitioned into 219 affine and 230 crystallographic space-group types, into 73 arithmetic and 32 geometric crystal classes, into 14 Bravais flocks (each Bravais flock consisting of the space groups with the same Bravais lattice type), into seven crystal systems, seven lattice systems and six crystal families. Similarly, the crystallographic point groups may be distributed into 73 arithmetic and 32 geometric crystal classes, seven crystal systems and six crystal families of point groups, whereas the set of all lattices is subdivided into 14 Bravais lattice types, seven lattice systems and again six crystal families of lattices. The different classifications are compared and their relations are discussed. Keywords: space groups; point groups; lattices; space-group types; arithmetic crystal classes; geometric crystal classes; Bravais classes; Bravais lattices; lattice types; Bravais flocks; crystal families; crystal systems; lattice systems