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Crystal lattices
International Tables for Crystallography (2016). Vol. A, ch. 3.1, pp. 698-719 [ doi:10.1107/97809553602060000929 ]
... last two sections of the chapter. 3.1.1. Bases and lattices H. Burzlaff a andH. Zimmermann e 3.1.1.1. Description and transformation of bases | | In three dimensions ... single finite polyhedron, namely the domain of influence (cf. Burzlaff & Zimmermann, 1977). 3.1.1.4. Special bases for lattices | | Different procedures ...
Generalized symmetry
International Tables for Crystallography (2016). Vol. A, Section 3.3.3.6, p. 790 [ doi:10.1107/97809553602060000931 ]
Generalized symmetry 3.3.3.6. Generalized symmetry The international symbols can be suitably modified to describe generalized symmetry, e.g. colour groups, which occur when the symmetry operations are combined with changes of physical properties. For the description of antisymmetry (or `black-white' symmetry), the symbols of the Bravais lattices are supplemented by additional ...
[more results from section 3.3.3 in volume A]
International short symbols
International Tables for Crystallography (2016). Vol. A, Section 3.3.2.5, p. 780 [ doi:10.1107/97809553602060000931 ]
... Natl Acad. Sci. USA, 58, 1768-1773. Donnay, J. D. H. (1969). Symbolism of rhombohedral space groups in Miller axes. Acta Cryst. A25, 715-716. Donnay, J. D. H. (1977). The structural classification of crystal point symmetries. Acta ...
[more results from section 3.3.2 in volume A]
Short symbols and generators
International Tables for Crystallography (2016). Vol. A, Section 3.3.1.4.3, pp. 778-779 [ doi:10.1107/97809553602060000931 ]
Short symbols and generators 3.3.1.4.3. Short symbols and generators If the symbols are not only used for the identification of a group but also for its construction, the symbol must contain a list of generating operations and additional relations, if necessary. Following this aspect, the Hermann-Mauguin symbols can be shortened. ...
[more results from section 3.3.1 in volume A]
Space-group symbols and their use
International Tables for Crystallography (2016). Vol. A, ch. 3.3, pp. 777-791 [ doi:10.1107/97809553602060000931 ]
... by additional symbols for mirror planes, if present. The subscripts h and v indicate mirror planes perpendicular and parallel to a ... tilde{3} †According to a private communication from J. D. H. Donnay, the symbols for elements of the second kind were ... 2h} D_{2h} D_{4h} D_{6h} D_{3d} O_{h} Hermann-Mauguin \bar{1} \displaystyle{2 \over m} \displaystyle{ ...
Example of Delaunay reduction and standardization of the basis
International Tables for Crystallography (2016). Vol. A, Section 3.1.2.4, pp. 707-708 [ doi:10.1107/97809553602060000929 ]
... Delaunay reduction. This example, given by B. Gruber (cf. Burzlaff & Zimmermann, 1985), shows the standardization problems remaining after the reduction. The ... sequence of [beta] and [gamma] can be interchanged: References Burzlaff, H. & Zimmermann, H. (1985). On the metrical properties of lattices. ...
[more results from section 3.1.2 in volume A]
Remarks
International Tables for Crystallography (2016). Vol. A, Section 3.1.1.5, pp. 699-700 [ doi:10.1107/97809553602060000929 ]
... e.g. a hexagonal cell centred at and which is called H. In this case, rule (iiia) above is violated as vectors ...
[more results from section 3.1.1 in volume A]
Changes introduced in space-group symbols since 1935
International Tables for Crystallography (2016). Vol. A, Section 3.3.4, p. 790 [ doi:10.1107/97809553602060000931 ]
... 1935), leads to C3m = C_{3v}^{1}; (ii) the hexagonal H-centred cell, with centring points in {\textstyle{2\over 3 ... .] Wolff, P. M. de, Billiet, Y., Donnay, J. D. H., Fischer, W., Galiulin, R. B., Glazer, A. M., Hahn, Th., Senechal, M., Shoemaker, D. P., Wondratschek, H., Wilson, A. J. C. & Abrahams, S. C. (1992). ...
International Tables for Crystallography (2016). Vol. A, ch. 3.1, pp. 698-719 [ doi:10.1107/97809553602060000929 ]
... last two sections of the chapter. 3.1.1. Bases and lattices H. Burzlaff a andH. Zimmermann e 3.1.1.1. Description and transformation of bases | | In three dimensions ... single finite polyhedron, namely the domain of influence (cf. Burzlaff & Zimmermann, 1977). 3.1.1.4. Special bases for lattices | | Different procedures ...
Generalized symmetry
International Tables for Crystallography (2016). Vol. A, Section 3.3.3.6, p. 790 [ doi:10.1107/97809553602060000931 ]
Generalized symmetry 3.3.3.6. Generalized symmetry The international symbols can be suitably modified to describe generalized symmetry, e.g. colour groups, which occur when the symmetry operations are combined with changes of physical properties. For the description of antisymmetry (or `black-white' symmetry), the symbols of the Bravais lattices are supplemented by additional ...
[more results from section 3.3.3 in volume A]
International short symbols
International Tables for Crystallography (2016). Vol. A, Section 3.3.2.5, p. 780 [ doi:10.1107/97809553602060000931 ]
... Natl Acad. Sci. USA, 58, 1768-1773. Donnay, J. D. H. (1969). Symbolism of rhombohedral space groups in Miller axes. Acta Cryst. A25, 715-716. Donnay, J. D. H. (1977). The structural classification of crystal point symmetries. Acta ...
[more results from section 3.3.2 in volume A]
Short symbols and generators
International Tables for Crystallography (2016). Vol. A, Section 3.3.1.4.3, pp. 778-779 [ doi:10.1107/97809553602060000931 ]
Short symbols and generators 3.3.1.4.3. Short symbols and generators If the symbols are not only used for the identification of a group but also for its construction, the symbol must contain a list of generating operations and additional relations, if necessary. Following this aspect, the Hermann-Mauguin symbols can be shortened. ...
[more results from section 3.3.1 in volume A]
Space-group symbols and their use
International Tables for Crystallography (2016). Vol. A, ch. 3.3, pp. 777-791 [ doi:10.1107/97809553602060000931 ]
... by additional symbols for mirror planes, if present. The subscripts h and v indicate mirror planes perpendicular and parallel to a ... tilde{3} †According to a private communication from J. D. H. Donnay, the symbols for elements of the second kind were ... 2h} D_{2h} D_{4h} D_{6h} D_{3d} O_{h} Hermann-Mauguin \bar{1} \displaystyle{2 \over m} \displaystyle{ ...
Example of Delaunay reduction and standardization of the basis
International Tables for Crystallography (2016). Vol. A, Section 3.1.2.4, pp. 707-708 [ doi:10.1107/97809553602060000929 ]
... Delaunay reduction. This example, given by B. Gruber (cf. Burzlaff & Zimmermann, 1985), shows the standardization problems remaining after the reduction. The ... sequence of [beta] and [gamma] can be interchanged: References Burzlaff, H. & Zimmermann, H. (1985). On the metrical properties of lattices. ...
[more results from section 3.1.2 in volume A]
Remarks
International Tables for Crystallography (2016). Vol. A, Section 3.1.1.5, pp. 699-700 [ doi:10.1107/97809553602060000929 ]
... e.g. a hexagonal cell centred at and which is called H. In this case, rule (iiia) above is violated as vectors ...
[more results from section 3.1.1 in volume A]
Changes introduced in space-group symbols since 1935
International Tables for Crystallography (2016). Vol. A, Section 3.3.4, p. 790 [ doi:10.1107/97809553602060000931 ]
... 1935), leads to C3m = C_{3v}^{1}; (ii) the hexagonal H-centred cell, with centring points in {\textstyle{2\over 3 ... .] Wolff, P. M. de, Billiet, Y., Donnay, J. D. H., Fischer, W., Galiulin, R. B., Glazer, A. M., Hahn, Th., Senechal, M., Shoemaker, D. P., Wondratschek, H., Wilson, A. J. C. & Abrahams, S. C. (1992). ...
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