International
Tables for Crystallography Volume C Mathematical, physical and chemical tables Edited by E. Prince © International Union of Crystallography 2006 |
International Tables for Crystallography (2006). Vol. C. ch. 9.7, pp. 903-904
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The symmorphic space groups are in a one-to-one correspondence with the arithmetic crystal classes, and each has at least one Wyckoff position with the full symmetry of the geometric crystal class. It would thus be possible for each symmorphic space group to accommodate molecules with the full symmetry of the point group corresponding to the geometric crystal class. With the obvious exceptions of P1 and , there seem to be no symmorphic space groups with primitive cells and one molecule only in the cell that do so, but the data of Belsky, Zorkaya & Zorky (1995
) show that about half the possibilities are realized in symmorphic space groups with centred cells. The situation is set out in Table 9.7.4.1
.
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Although about half the point groups are not represented in symmorphic space groups with one molecule in the appropriate special position, it is interesting to look for molecules of these symmetries in space groups of higher symmetry. A few are in fact to be found in non-symmorphic space groups, but seven point groups have no established examples.
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