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  • Reference work
  • © 2002

International Tables for Crystallography, Volume A: Space Group Symmetry


  • Volume A of International Tables for Crystallography is the definitive source of information on crystallographic symmetry

  • Contains extensive tabulations of data for and illustrations of the 17 plane groups, the 230 space groups and the 32 crystallographic point groups

  • The use of these diagrams and data is explained in the first part of the volume with the aid of many examples in a way that is instructive and accessible to research students solving their first crystal structure

  • The second part of the volume is pitched at a much higher theoretical level and comprises an advanced textbook on crystallographic symmetry in direct or physical space, allowing the expert crystallographer to make maximum use of the information in the tables

  • Indispensible compendium of information for professional crystallographers and for all chemists, physicists, mineralogists, biologists or material scientists who employ crystallographic methods and who are concerned with the structure and the properties of crystalline materials

Part of the book series: International Tables for Crystallography (IUCR, volume A)

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Table of contents (37 entries)

  1. Front Matter

    Pages i-xx
  2. Guide to the use of the space-group tables

    1. Classification and coordinate systems of space groups

      • Th. Hahn, A. Looijenga-Vos
      Pages 14-16
    2. Contents and arrangement of the tables

      • Th. Hahn, A. Looijenga-Vos
      Pages 17-41
  3. Determination of space groups

    1. Space-group determination and diffraction symbols

      • A. Looijenga-Vos, M. J. Buerger
      Pages 44-54
  4. Synoptic tables of space-group symbols

    1. Introduction to the synoptic tables

      • E. F. Bertaut
      Pages 56-60
    2. Symbols for space groups

      • E. F. Bertaut
      Pages 62-76
  5. Transformations in crystallography

  6. The 17 plane groups (two-dimensional space groups)

  7. The 230 space groups

    1. The 230 space groups

      • Th. Hahn
      Pages 112-717
  8. Introduction to space-group symmetry

    1. Basic concepts

      • H. Wondratschek
      Pages 720-725
    2. Special topics on space groups

      • H. Wondratschek
      Pages 732-740
  9. Crystal lattices

    1. Bases, lattices, Bravais lattices and other classifications

      • H. Burzlaff, H. Zimmermann
      Pages 742-749
    2. Reduced bases

      • P. M. de Wolff
      Pages 750-755

About this book

Volume A treats crystallographic symmetry in direct or physical space.

The first five parts of the volume contain introductory material: lists of symbols and terms; a guide to the use of the space-group tables; the determination of space groups; synoptic tables of space-group symbols; and unit-cell (coordinate) transformations. These are followed by the plane-group and space-group tables.

The rest of the volume is at a much higher theoretical level than Parts 1 to 5; it has many features of an advanced textbook of crystallography. Parts 8 to 15 deal with the following aspects of symmetry theory: the mathematical approach to space groups; crystal lattices; point groups and crystal classes; symbols for symmetry operations; symbols for space groups; isomorphic subgroups of space groups; lattice complexes; and normalizers of space groups.

Volume A is designed not only for professional crystallographers, but also for chemists, physicists, mineralogists, biologists and material scientists who employ crystallographic methods and who are concerned with the structure and the properties of crystalline materials.

The fifth edition of Volume A has been reviewed by P. Paufler [Acta Cryst. (2004). A60, 641-642]. The first edition was reviewed by K. M. Stadnicka, B. J. Oleksyn and K. Z. Sokalski [Acta Cryst. (1987). A43, 156-159].

International Tables for personal use can be purchased at a discount. Contact Customer Service for further information and to place an order.


  • classification
  • crystal
  • crystallography
  • diffraction
  • formation
  • material
  • mineral
  • point group
  • structure
  • symmetry
  • mineral resources


From the reviews:

"... The Editor's goal to provide data that are useful for all aspects of crystallography as well as text to satisfy the needs of those interested in the theoretical reasons behind these tables has led to a fruitful combination of tables for practical use in the first part and a high-level textbook in the second.

To sum up, ITA is not only the first and the most frequently edited volume in this series of a new generation of crystallographic references, it sets standards for the subject of crystallography in general as a `hard' and far-reaching branch of science. Thanks to the availability of this reference, supported by the IUCr, there is nowadays an international consensus on key concepts of crystallography. ITA is a book of symbols relevant for symmetry properties of crystals. While many other books are using the relevant symbols, ITA delivers not only the complete listings but also a comprehensive explanation of the theory behind them and detailed instructions for use. Hence, it is indispensable for people dealing with the symmetry of crystals." (P. Paufler [Acta Cryst. (2004). A60, 641-642] )

Editors and Affiliations

  • Institut für Kristallographie, Rheinisch-Westfälische Technische Hochschule, D-52056 Aachen, Germany

    Th. Hahn

Bibliographic Information