Symmetry. Fundamentals of Crystallography

  • I. S. Zheludev


A. Definitions and Basic Concepts. Symmetryis the property of geometrical figures which have identical and regularly distributed parts. We shall consider only finite figures although there is, in general, no limitation to the size of a figure in point symmetry. The laws governing the uniform distribution of equal parts in a figure are given by symmetry operations or symmetry transformations. The science of symmetry shows that symmetry transformations of three-dimensional figures are simple (proper) rotation and rotation accompanied by reflection (improper or reflection rotation).*


Symmetry Group Symmetry Transformation Symmetry Operation Symmetry Element Point Symmetry Group 


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  1. 1.
    N. V. Belov, Structural Crystallography [in Russian], Izd. AN SSSR, Moscow (1951).Google Scholar
  2. 2.
    G. B. Bokii, Introduction to Crystal Chemistry [in Russian], Izd. MGU, Moscow (1954).Google Scholar
  3. 3.
    B. N. Delone, N. Padurov, and A. Aleksandrov, Mathematical Fundamentals of Crystal Structure Analysis and X-ray Determination of Unit Cells [in Russian], GTTI, Moscow-Leningrad (1934).Google Scholar
  4. 4.
    I. S. Zheludev, Kristallografiya, 2(6):728 (1957).MathSciNetGoogle Scholar
  5. 5.
    G. S. Zhdanov, Crystal Physics, Oliver and Boyd, Edinburgh-London (1965).Google Scholar
  6. 6.
    E. E. Flint, Practical Handbook on Geometrical Crystallography, 3rd ed. [in Russian], Nedra, Moscow (1956).Google Scholar
  7. 7.
    A. V. Shubnikov, Symmetry and Antisymmetry of Finite Figures [in Russian], Izd. AN SSSR, Moscow (1951).Google Scholar
  8. 8.
    A. V. Shubnikov, E. E. Flint, and G. B. Bokii, Principles of Crystallography [in Russian], Izd. AN SSSR, Moscow (1940).Google Scholar

Copyright information

© Plenum Press, New York 1971

Authors and Affiliations

  • I. S. Zheludev
    • 1
  1. 1.Institute of CrystallographyThe Academy of Sciences of the USSRMoscowUSSR

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