Plane and Frieze Symmetry Group Determination for Educational Purposes

Three-dimensional symmetry plays a crucial role in crystallography education. The educational process can be facilitated by introducing the analysis of friezes and plane patterns such as parquets before presenting more sophisticated crystal structures. Analysis of the symmetry of parquets can serve as an opportunity to follow the full routine of finding symmetry group symbols through incorporation of a two-step procedure involving the determination of Bravais lattice type. The aim of this paper is to provide a simple description of the analysis of Bravais lattices and pattern symmetry that can be used by students as well as crystallography educators. The procedure is also summarized in the form of comprehensive tree charts. This form is easy to use and popular with students. It may also aid in the retention of certain facts concerning crystallographic methodology. Examples of patterns in frieze and parquet forms were taken from the interiors of Kórnik Castle (Poland), which exhibit Moorish-style ornamentation including dichroic patterns and constitute an important locus of cultural heritage capable of strengthening students' motivation.