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After a discussion of the historical background and of the properties of structural descriptors, the concept of mappings is applied to establish and quantify geometrical relationships among crystal structures. Mappings that lead to relationships are called similarity operators. Thus, all structures belonging to the same structure type can be collected, e.g. from the data of a data bank, by suitable similarity operators. Moreover, different structure types may be grouped into structure families using the same technique. A procedure is described to complete a similarity operator for a pair of structures if a relationship is present. A practical example is presented; further applications will be given in a separate paper.
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