Point groups and crystal classes

Section 3.2.1 treats the geometric and group-theoretical aspects of both crystallographic and noncrystallographic point groups. It includes descriptions and diagrams of the sub- and supergroups of the crystallographic point groups and tabulations and diagrams of the (infinitely many) noncrystallographic point groups and their subgroups, with special emphasis on the two icosahedral point groups. All entries and terms are thoroughly described in the text. Section 3.2.2 discusses the relations between symmetry and the physical properties of crystals. The following properties and their dependence on the crystallographic point-group symmetries are described and presented in several tables: crystal morphology, symmetry of etch figures, optical birefringence, optical activity, enantiomorphism, pyroelectricity (ferroelectricity) and piezoelectricity. Section 3.2.3 presents an extensive tabulation of the 10 two-dimensional and the 32 three-dimensional crystallographic point groups, containing for each group the stereographic projections of the symmetry elements and the face poles of the general crystal form, and a table with the Wyckoff positions, their site symmetries and the coordinates of symmetry-equivalent points, and, in addition, the names and Miller indices {hkl} of the general and special face and point forms. Each point-group table concludes with the three major projection symmetries. Section 3.2.4 discusses molecular symmetry, including noncrystallographic symmetries, the symmetry of polymeric molecules and symmetry aspects of chiral molecules and crystal structures. It includes a table of the crystallographic and noncrystallographic rod groups.