Symmetry elements in space groups and point groups. Addenda to two IUCr reports on the nomenclature of symmetry

The definition of 'symmetry element' given in the Report of the IUCr Ad-Woe Committee on the Nomenclature of Symmetry by de Wolff et nl. [Acta Cryst. (1989). A45, 494-499] is shown to contain an ambiguity in the case of space groups P6/m, P6/mmm, P6/mcc and point groups 6/m and 6/mmm. The ambiguity is removed by redefining the 'geometric element' as a labelled geometric item in which the label is related to the rotation angle of the rotation or rotoinversion symmetry operation. The complete set of different types of glide plane is shown to contain three more than the 15 that are illustrated in the 1992 Report by de Wolff et al. [Acta Cryst. (1992). A48, 727-732].