Lattice complexes and limiting complexes versus orbit types and non-characteristic orbits: a comparative discussion

The concept of lattice complexes is compared with the concept of orbit types, and the correspondences and differences are worked out in some detail. For this, it turned out to be necessary to distinguish whether a set of symmetrically equivalent points is regarded as attached to or as detached from its generating space group. The terms 'crystallographic orbit' and 'point configuration' used as synonyms so far are applied here to discriminate between these distinct meanings. On this basis, the terminology within both concepts is redefined stressing the aspect of equivalence classes. After that, the relations between non-characteristic orbits and limiting complexes are carefully discussed for the first time.