Bilbao Crystallographic Server Retrieval Tools Help Symmetry Operation

Symmetry operations

This program calculates the geometric interpretation of matrix column representation of symmetry operation for a given crystal system or space group. You have differents ways to use it.

If you want to work on a standard/default setting, just click on [Standard/Default Setting]].

If you want to obtain the symmetry operation in an arbitrary setting, click on [User-Defined Setting]. This will show a form where you should give the transformation matrix relating the standard/default setting of the group you have chosen with the new setting.

Your can click on [ITA Settings] and choose the space group symbols listed in International Tables for Crystallography, Vol.A.


i) The crystal system or the space group number.

The space groups are specified by their number as given in the International Tables for Crystallography, Vol. A. You can give this number if you know it, or you can choose it from the table with the space group numbers and symbols if you click on [Choose it].

ii) The matrix column representation of symmetry operation.

You can introduce it in coordinate triplets or in matrix form.

iii) The transformation matrix.

We only have to introduce the transformation matrix if we want to work on a non conventional setting.


With this program we obtain:

  • The symbol of the symmetry operation.
  • The intrinsic translation part if it has.
  • The location of the symmetry element.

  • Bilbao Crystallographic Server
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