Symmetry database help

The symmetry database provides access to the data from International Tables for Crystallography Volumes A and A1 and allows simple calculations using the data to be performed. These calculations include generator and general-position transformations, Wyckoff-position transformations and some group-subgroup pair calculations such as coset decomposition and Wyckoff-position splittings.


The following symbols are used in the symmetry database:
Help 471f2019e34cbeb5ac1afec91f5ba32a69712c7776eaf4b2fa01126090773f7b The info symbol indicates that there is a help page providing more information about the data presented on the current page. Click on the symbol to see this information.
Flecha down c8793e7cca1b8f3ee6803aef1ce37d20de13ef770cfc4e63e7d9160f2e78ad2a Click on the slide down symbol to see some additional information related to the current page.
Flecha up a65d94e9a76e85357af003266f3853173867bb8a22bcfefbf39a666e6a6e90d6 Click on the slide up symbol to hide the additional information shown after you have clicked on the slide down symbol.
Indicator 5165b05b5f9bf55f906f9b194dcdbb1b4c55f4b9169c0418f1bfd8de5d62ec3f This symbol is shown to indicate that a calculation is in process. If you see this symbol, please wait until the calculation is finished and the result is shown.

Default settings

The conventions used for the default settings of the space groups are:

  • for monoclinic groups: unique axis b, cell choice 1;
  • for orthorhombic groups: the 'standard setting' as defined in Section of Volume A (or Section 2.2.6 in the first online edition of Volume A);
  • for space groups with two origin choices: origin choice 2;
  • for trigonal space groups: hexagonal axes.

For space groups with more than one conventional setting, a 'Change setting' button is provided:

When you click on this button, a list of the conventional settings is shown. When you select a specific setting, the corresponding data for the selected setting are shown.

Data transformations

On the pages that show data that can be transformed to a non-conventional basis, a 'Transform' button is provided:

Clicking on the button opens a form in which the axes transformation and the origin shift can be entered:

The origin-shift coordinates can be specified with real numbers or fractions: e.g. 0.5 or 1/2.

Once the transformation information has been entered, click on the 'Change basis' button to see the transformed group data.