Other symmetries

Wilson, A. J. C.; Karen, V. L.; Mighell, A.

doi:10.1107/97809553602060000623

International
Tables for
Crystallography
Volume C
Mathematical, physical and chemical tables
Edited by E. Prince

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International Tables for Crystallography (2006). Vol. C. ch. 9.7, p. 903

Section 9.7.4.3. Other symmetries

A. J. C. Wilson,^a ^‡ V. L. Karen^b and A. Mighell^b

^a St John's College, Cambridge CB2 1TP, England, and ^bNIST Center for Neutron Research, National Institute of Standards and Technology, Gaithersburg, MD 20899, USA

9.7.4.3. Other symmetries

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Table 9.7.2.1 gives statistics for the number of space groups possessing Wyckoff positions of symmetry $[{\cal G}]$ , where $[{\cal G}]$ is one of the 32 point groups, the number exhibiting structures of some kind, and the number in which the special position of symmetry $[{\cal G}]$ is actually used. It has to be remembered that this table represents the state of knowledge in 1994, that there may be small errors in the counts in the second column, and that new structures will gradually increase the numbers in the third and fourth columns. Nevertheless, some trends are clear. The arrangement of the point groups is in ascending order of their `order' (Hahn, 2005, Section 10.1.4.1 ), and all numbers show a general decrease with increasing order. When molecular symmetry is used, the favourite is the diad axis 2, closely followed by the mirror plane m, with the centre of symmetry $[\overline {1}]$ , the triad axis 3 and the tetrad inversion axis $[\overline {4}]$ trailing. It must also be remembered that these data are for numbers of space groups, not numbers of structures.

References

Hahn, Th. (2005). Editor. International tables for crystallography, Vol. A, Space-group symmetry, fifth edition. Heidelberg: Springer.Google Scholar

International Tables for Crystallography (2006). Vol. C. ch. 9.7, p. 903