Die Gitterkomplexe der Ebenengruppen

The concept of lattice complexes due to C. Hermann is applied to the sets of equivalent points in planar groups. Based on his nomenclature for invariant lattice complexes a symbolism is derived with the use of symbols for point complexes and their arrangement in addition. It is possible to construct each lattice complex from its symbol. The concept can be applied to space groups. All of these lattice complexes are tabulated together with their sets of equivalent points. Some applications are discussed. The efficiency of the conception is demonstrated by tables containing the relations between sets of equivalent points in different planar groups.