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New developments of the symmetry database


The symmetry database at has been updated and expanded to include a wealth of new data. Information is now available for the Euclidean, chirality-preserving and affine normalizers of the space groups; these aid many crystallographic calculations, including the comparison of different but equivalent coordinate descriptions of a crystal structure (and the accompanying changes in structure factors) and the derivation of phase restrictions for use in direct methods, as described in Chapter 3.5 of the new edition of International Tables Volume A ( For those interested in molecular symmetry and the physical properties of materials, the generators, general and special positions, and Wyckoff positions of the three-dimensional crystallographic point groups are presented and can be transformed to different settings, enhancing and extending the data presented in Chapter 3.2 of Volume A. Users will also enjoy the simple, clear and instructive interactive visualization of the symmetry elements of the crystallographic point groups.

Throughout the database, symmetry operations are now presented in four different ways to suit a range of purposes: as x, y, z-based coordinate triplets, in matrix form, by geometric symbols (indicating the type and order of the operations, and the orientation of the corresponding symmetry elements) and in Seitz notation. Site-symmetry groups, whose oriented symbols show how the symmetry elements at a site are related to the symmetry directions of the crystal lattice, are now also listed for the space and point groups.

The symmetry database allows the generation of data for any space-group setting (not just those included in Volumes A and A1). The point-group visualization allows the user to turn different symmetry elements on and off and rotate the view so one can see the position of the planes and axes; it makes an excellent teaching tool.

The symmetry database is available to institutions that have access to International Tables Online. Please see