On the equivalence of point configurations due to Euclidean normalizers (Cheshire groups) of space groups

The Euclidean normalizers of space groups form the appropriate mathematical tool for several problems treated independently by crystallographers in the past, e.g. the comparison, the classification and the standardized description of crystal structures. Explicit tables are presented that enable the user to handle Euclidean normalizers in an easy way and, especially, to calculate all descriptions of a crystal structure compatible with a chosen space-group setting. The use of the tables is illustrated by different examples, and the role of Euclidean normalizers for crystal-structure determination is discussed.