Advertisement

Space-Group Symmetries

Abstract

Up to this point, structures of mostly finite objects have been discussed. Thus, point groups were applicable. A simplified compilation of various symmetries was presented in Figure 2-41 and Table 2-2. The point-group symmetries are characterized by the lack of periodicity in any direction. Periodicity may be introduced by translational symmetry. If periodicity is present, space groups are applicable for the symmetry description. There is a slight inconsistency here in the terminology. Even a three-dimensional object may have point-group symmetry. On the other hand, the so-called dimensionality of the space group is not determined by the dimensionality of the object. Rather, it is determined by its periodicity. The following groups are space-group symmetries, where the superscript refers to the dimensionality of the object and the subscript to the periodicity.

Keywords

Symmetry Element Symmetry Class Screw Axis Translation Axis Photograph Courtesy 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. [8-1]
    F. J. Budden, The Fascination of Groups, Cambridge University Press, Cambridge (1972).Google Scholar
  2. [8-2]
    A. V. Shubnikov and V A. Koptsik, Symmetry in Science and Art, Plenum Press, New York (1974). [Russian original: Simmetriya v nauke i iskusslve, Nauka, Moscow (1972).]Google Scholar
  3. [8-3]
    I. Hargittai and G. Lengyel, J. Chem. Educ. 61, 1033 (1984).Google Scholar
  4. [8-4]
    I. Hargittai, in Symmetrie in Geistes-und Naturwissenschaft (R. Wille, ed.), Springer-Verlag, Berlin (1988).Google Scholar
  5. [8-5]
    D. W. Crowe, in The Geometric Vein. The Coxeter Fertschrift (C. Davis, B. Grünbaum, and F. A. Sherk, eds.), Springer-Verlag, New York (1982).Google Scholar
  6. [8-6]
    K. Peters, W. Ott, and H. G. v. Schnering, Angew. Chem. Int. Ed. Engl. 21, 697 (1982).CrossRefGoogle Scholar
  7. [8-7]
    H. Tadokoro, Structure of Crystalline Polymers, Wiley-Interscience, New York (1979).Google Scholar
  8. [8-8]
    P. Doty, in The Molecular Basis of Life (R. H. Haynes and P. C. Hanewalt, eds.), W. H. Freeman and Co., San Francisco (1968).Google Scholar
  9. [8-9]
    B. K. Vainshtein, V. M. Fridkin, and V. L. Indenbom, Sovremennaya Kristallografiya, Vol. 2, Struktura Kristallov, Nauka, Moscow (1979).Google Scholar
  10. [8-10]
    B. P. Belousov, in Sbornik Referatov po Radiatsionnoi Medicine, pp. 145–147, Medgiz, Moscow (1958).Google Scholar
  11. [8-11]
    A M. Zhabotinsky, Biofizika 9, 306 (1964).Google Scholar
  12. [8-12]
    E. Körös, in Spiral Symmetry (I. Hargittai and C. A. Pickover, eds.), p. 221, World Scientific, Singapore (1992).Google Scholar
  13. [8-13]
    B. G. Elmegreen, in Spiral Symmetry (I. Hargittai and C. A. Pickover, eds), p. 95, World Scientific, Singapore (1992); B. G. Elmegreen, D. M. Elmegreen, and P. E. Seiden, Astrophys. J. 343, 602 (1989).Google Scholar
  14. [8-14]
    Y. Ronen and P. Rozenak, J.. Mater. Sci. 28, 5576 (1993).CrossRefGoogle Scholar
  15. [8-15]
    A. V. Shubnikov, Sov. Phys. Crystallogr. 5, 469 (1961); reprinted in Crystal Symmetries (I. Hargittai and B. K. Vainshtein, eds.), p. 365, Pergamon Press, Oxford (1988).Google Scholar
  16. [8-16]
    M. J. Buerger, Elementary Crystallography, An Introduction to the Fundamental Geometrical Features of Crystals, 4th printing, John Wiley & Sons, New York (1967).Google Scholar
  17. [8-17]
    I. Hargittai and G. Lengyel, J. Chem. Educ. 62, 35 (1985).CrossRefGoogle Scholar
  18. [8-18]
    L. V. Azaroff, Introduction to Solids, McGraw-Hill, New York (1960).Google Scholar
  19. [8-19]
    A. Holmes, Principles of Physical Geology, The Ronald Press Co., New York (1965).Google Scholar
  20. [8-20]
    E. Gregory, Proc. IEEE 77, 1110 (1989).CrossRefGoogle Scholar
  21. [8-21]
    D. Schattschneider, Visions of Symmetry, Notebooks, Periodic Drawings, and Related Work of M. C. Escher, W. H. Freeman and Co., New York (1990).Google Scholar
  22. [8-22]
    C. H. MacGillavry, Symmetry Aspects of M. C. Escher’s Periodic Drawings, Bohn, Scheltema and Holkema, Utrecht (1976).Google Scholar
  23. [8-23]
    F. Brisse, Can. Mineral. 19, 217 (1981).Google Scholar
  24. [8-24]
    G. Pólya, Z. Kristallogr. 60, 278 (1924).Google Scholar
  25. [8-25]
    I. El-Said and A. Parman, Geometric Concepts in Islamic Art, World of Islam Festival Publ. Co., London (1976).Google Scholar
  26. [8-26]
    P. D’Avennes (ed.), Arabic Art Color, Dover, New York (1978).Google Scholar
  27. [8-27]
    Kh. S. Mamedov, I. R. Amiraslanov, G. N. Nadzhafov, and A. A. Muzhaliev, Decoralions Remember, Azerneshr, Baku (1981) [in Azerbaijani].Google Scholar
  28. [8-28]
    B. Grünbaum and G. C. Shephard, Tilings and Patterns, W. H. Freeman and Co., New York (1987).Google Scholar
  29. [8-29]
    A. H. Fraser, J. Opt. Soc. Am. 73, 1626 (1983).CrossRefGoogle Scholar
  30. [8-30]
    M. Ge and K. Sattler, Science 260, 515 (1993); J. Xhie, K. Sattler, M. Ge, and N. Venkateswaran, Phys. Rev. B 47, 15835 (1993).CrossRefPubMedGoogle Scholar
  31. [8-31]
    H. Giger, in Symmetry, Unifying Human Understanding (I. Hargittai, ed.), p. 329, Pergamon Press, New York (1986).Google Scholar
  32. [8-32]
    W. Witschi, in Symmetry, Unifying Human Understanding (I. Hargittai, ed.), p. 363, Pergamon Press, New York (1986).Google Scholar

Copyright information

© Plenum Press 1995

Personalised recommendations