Some references about crystallographic definitions and conventions are shown below. Though spglib may not follow them fully, it doesn’t mean spglib doesn’t respect them, rather it is due to spglib-author’s lack of understanding the crystallography ashamedly.

General materials#


M. I. Aroyo, editor. International Tables for Crystallography. Volume A. International Union of Crystallography, December 2016. URL:, doi:10.1107/97809553602060000114.


Ulrich Müller. Symmetry relationships between crystal structures: applications of crystallographic group theory in crystal chemistry. Volume 18. OUP Oxford, 2013.


Michael Glazer, Gerald Burns, and Alexander N Glazer. Space groups for solid state scientists. Elsevier, 2012.

Specific algorithms#


R. W. Grosse-Kunstleve. Algorithms for deriving crystallographic space-group information. Acta Cryst. A, 55(2-2):383–395, 1999. doi:


R. W. Grosse-Kunstleve and P. D. Adams. Algorithms for deriving crystallographic space-group information. II. Treatment of special positions. Acta Cryst. A, 58(1):60–65, Jan 2002. URL:, doi:10.1107/S0108767301016658.

Setting and standardization#


S. R. Hall. Space-group notation with an explicit origin. Acta Cryst. A, 37(4):517–525, Jul 1981. URL:, doi:10.1107/S0567739481001228.


E Parthé and LM Gelato. The standardization of inorganic crystal-structure data. Acta Crystallographica Section A: Foundations of Crystallography, 40(3):169–183, 1984.


Erwin Parthé, Karin Cenzual, and Roman E. Gladyshevskii. Standardization of crystal structure data as an aid to the classification of crystal structure types. Journal of Alloys and Compounds, 197(2):291–301, 1993. Proceeding of the Workshop on Regularities, Classifications and Prediction of Advanced Materials. URL:, doi:


E Parthé and LOUISE M Gelato. The'best'unit cell for monoclinic structures consistent with b axis unique and cell choice 1 ofinternational tables for crystallography (1983). Acta Crystallographica Section A: Foundations of Crystallography, 41(2):142–151, 1985.

Magnetic space group#


Javier González-Platas, Nebil A. Katcho, and Juan Rodríguez-Carvajal. Extension of Hall symbols of crystallographic space groups to magnetic space groups. Journal of Applied Crystallography, 54(1):338–342, Feb 2021. URL:, doi:10.1107/S1600576720015897.


Samuel V. Gallego, J. Manuel Perez-Mato, Luis Elcoro, Emre S. Tasci, Robert M. Hanson, Koichi Momma, Mois I. Aroyo, and Gotzon Madariaga. \it MAGNDATA: towards a database of magnetic structures. I.The commensurate case. Journal of Applied Crystallography, 49(5):1750–1776, Oct 2016. URL:, doi:10.1107/S1600576716012863.


Branton J. Campbell, Harold T. Stokes, J. Manuel Perez-Mato, and Juan Rodríguez-Carvajal. Introducing a unified magnetic space-group symbol. Acta Crystallographica Section A, 78(2):99–106, Mar 2022. URL:, doi:10.1107/S2053273321012912.


Daniel B Litvin. Magnetic group tables. IUCr, 2014. URL:

Mathematical treatment#


Bernd Souvignier. Group theory applied to crystallography. URL:


J. Opgenorth, W. Plesken, and T. Schulz. Crystallographic Algorithms and Tables. Acta Cryst. Section A, 54(5):517–531, Sep 1998. URL:, doi:10.1107/S010876739701547X.


Bettina Eick and Bernd Souvignier. Algorithms for crystallographic groups. International Journal of Quantum Chemistry, 106(1):316–343, 2005. URL:, doi:10.1002/qua.20747.


B. Eick, F. Gähler, and W. Nickel. Computing Maximal Subgroups and Wyckoff Positions of Space Groups. Acta Crystallographica Section A, 53(4):467–474, Jul 1997. URL:, doi:10.1107/S0108767397003462.


Howard Hiller. Crystallography and cohomology of groups. The American Mathematical Monthly, 93(10):765–779, 1986. URL: