Tables of (3+d)-Dimensional Superspace Groups

Harold T. Stokes and Branton J. Campbell, Department of Physics and Astronomy, Brigham Young University, Provo, Utah, 84602, USA,
Sander van Smaalen, University of Bayreuth, Bayreuth, Germany,

Description: Tables of (3+d)-dimensional superspace groups (d=1,2,3) and tools for finding standard settings and for transforming a superspace group to new settings.
Version History
How to cite ISO(3+d)D: ISOTROPY Software Suite,
Also H. T. Stokes, B. J. Campbell, and S. van Smaalen, "Generation of (3+d)-Dimensional Superspace Groups for Describing the Symmetry of Modulated Crystalline Structures." Acta Cryst. A, 67, 45-55 (2011).
And S. van Smaalen, B. J. Campbell, and H. T. Stokes, "Equivalence of Superspace Groups." Acta Cryst. A, 69, 75-90 (2013).

Select Notation

Default notation is x,y,z,t,...
Change notation to x1,x2,x3,x4,... or xs1,xs2,xs3,xs4,...


(1) List of Bravais classes and superspace groups (pdf files)

(2) Description of each Bravais class and each superspace group (zip file containing text files)

(3) Data file (zip file containing text file which can be read by a computer program such as the Fortran 90 program read_ssg_datafile.f)

Detailed information

(1) Choose group from list

(2) Enter superspace group number:

Finder tool

FINDSSG: enter centering translations and operators in any setting.

Transformation tool

TRANSFORMSSG: transform superspace group to an arbitrary setting.

Disclaimer and copyright notice


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Copyright notice

© 2010 Harold T. Stokes, Branton Campbell and Sander van Smaalen.

The use of information obtained from this web site is authorised, provided the source is acknowledged. The redistribution of information, for example but not restricted to complete tables of superspace groups, is not allowed.