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International
Tables for Crystallography Volume A Space-group symmetry Edited by Th. Hahn © International Union of Crystallography 2006 |
International Tables for Crystallography (2006). Vol. A. ch. 8.3, pp. 732-740
https://doi.org/10.1107/97809553602060000516 Chapter 8.3. Special topics on space groups
a
Institut für Kristallographie, Universität, D-76128 Karlsruhe, Germany |
Footnotes
1
Also space group ![[P4_{2}/ncm \equiv D_{4h}^{16}]](/teximages/abch8o3/abch8o3fi25.svg)
(No. 138) is listed with two origins. The first origin is chosen at a point with site symmetry ![[\bar{4}]](/teximages/abch1o4/abch1o4fi129.svg)
as in Hermann (1935)![[link]](/graphics/greenarr.gif)
. The site symmetries ![[(2/m)]](/teximages/abch2o2/abch2o2fi583.svg)
of the centres of inversion have the same order 4.
2 Instead of `site-symmetry group', the term `point group' is frequently used for the local symmetry in a crystal structure or for the symmetry of a molecule. In order to avoid confusion, in this chapter the term `point group' is exclusively used for the symmetry of the external shape and of the physical properties of the macroscopic crystal, i.e. for a symmetry in vector space.
3 For the term `conjugate subgroups', see Section 8.3.6.
4 For the crystallographic orbits different names have been used by different authors: regelmässiges Punktsystem, Sohncke (1879) and Schoenflies (1891); regular system of points, Fedorov (1891); Punktkonfiguration, Fischer & Koch (1974); orbit, Wondratschek (1976); point configuration, Fischer & Koch (1978) and Part 14
of this volume; crystallographic orbit, Matsumoto & Wondratschek (1979) and Wondratschek (1980).
5 Fischer & Koch (1974) use the name Punktlage.
6 Section 8.3.6 and Part 15
deal with normalizers of space groups in more detail.
7 Hermann (1929) used the term zellengleich but this term caused misunderstandings because it was sometimes understood to refer to the conventional unit cell. Not the conservation of the conventional unit cell but rather the retention of all translations of the space group is the essential feature of t subgroups.
(No. 138) is listed with two origins. The first origin is chosen at a point with site symmetry as in Hermann (1935). The site symmetries of the centres of inversion have the same order 4.2 Instead of `site-symmetry group', the term `point group' is frequently used for the local symmetry in a crystal structure or for the symmetry of a molecule. In order to avoid confusion, in this chapter the term `point group' is exclusively used for the symmetry of the external shape and of the physical properties of the macroscopic crystal, i.e. for a symmetry in vector space.
3 For the term `conjugate subgroups', see Section 8.3.6
.4 For the crystallographic orbits different names have been used by different authors: regelmässiges Punktsystem, Sohncke (1879)
and Schoenflies (1891); regular system of points, Fedorov (1891); Punktkonfiguration, Fischer & Koch (1974); orbit, Wondratschek (1976); point configuration, Fischer & Koch (1978) and Part 14
of this volume; crystallographic orbit, Matsumoto & Wondratschek (1979) and Wondratschek (1980).5 Fischer & Koch (1974)
use the name Punktlage.6 Section 8.3.6
and Part 15
deal with normalizers of space groups in more detail.7 Hermann (1929)
used the term zellengleich but this term caused misunderstandings because it was sometimes understood to refer to the conventional unit cell. Not the conservation of the conventional unit cell but rather the retention of all translations of the space group is the essential feature of t subgroups.