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Abstract

A `geometric element ' is defined, for any given symmetry operation, as a geometric item that allows the operation (after removing any intrinsic translation) to be located and oriented. In the case of an inversion, a (screw-) rotation or a (glide-) reflection, it is respectively a point, line or plane. In the case of a rotoinversion, the geometric element consists of the axis of the rotation part and the center of the inversion part. As a general concept, the geometric element may be justified by a mathematical definition (as given in the Appendix). A `symmetry element ' (of a given crystal structure or object) is defined as a concept with a double meaning, namely the combination of a geometric element with the set of symmetry operations having this geometric element in common (`element set'). There is no overlap between element sets of a given structure. Together with the identity and the translations, for which a geometric element is not defined, the element sets cover all symmetry operations.

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