Space Group Symmetry

Abstract

Thus far the treatment of symmetry has been restricted to the proper rotational and reflection symmetries of space lattices. The discussion of the symmetry of crystalline solids does not end with the presentation of the 14 Bravais lattice types because the symmetry of a solid is the symmetry of its three-dimensionally periodic particle density, and there are more symmetries available to such periodic patterns than to the lattices which characterize their translational symmetries. This is in part because the pattern need not be centrosymmetric while the lattice must be, and in part because of the existence of symmetry operations appropriate to such patterns but not to their lattices.