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Lattice complexes
International Tables for Crystallography (2016). Vol. A, ch. 3.4, pp. 792-825 [ doi:10.1107/97809553602060000932 ]
... definition used in this chapter was proposed later still by Fischer & Koch (1974a) [cf. also Koch & Fischer (1978a)]. An alternative definition was given by Zimmermann & Burzlaff ... space groups belong to different types. The terms `point configuration' (Fischer & Koch, 1974a) and `crystallographic orbit' (Matsumoto & Wondratschek, 1979) have ...
Reduction of the parameter regions to be considered for geometrical studies of point configurations
International Tables for Crystallography (2016). Vol. A, Section 3.5.3.5, p. 850 [ doi:10.1107/97809553602060000933 ]
... Dirichlet domains etc.), the Euclidean normalizers (cf. e.g. Laves, 1931; Fischer, 1971, 1991; Koch, 1984a) as well as the affine normalizers (cf. Fischer, 1968) of the space groups allow a further reduction of ... Fig. 3.5.2.1) by means of the affine normalizer . References Fischer, W. (1968). Kreispackungsbedingungen in der Ebene. Acta Cryst. ...
[more results from section 3.5.3 in volume A]
Affine normalizers of plane groups and space groups
International Tables for Crystallography (2016). Vol. A, Section 3.5.2.2, pp. 830-838 [ doi:10.1107/97809553602060000933 ]
Affine normalizers of plane groups and space groups 3.5.2.2. Affine normalizers of plane groups and space groups The affine normalizer of a space (plane) group either is a true supergroup of its Euclidean normalizer , or both normalizers coincide: As any translation is an isometry, each translation belonging to also belongs to ...
[more results from section 3.5.2 in volume A]
Definitions
International Tables for Crystallography (2016). Vol. A, Section 3.5.1.2, pp. 826-827 [ doi:10.1107/97809553602060000933 ]
... been tabulated in more detail by Gubler (1982a,b) and Fischer & Koch (1983). The Euclidean normalizers of triclinic and monoclinic ... Wyckoff sets and the definition of lattice complexes by Koch & Fischer (1975), even though there the automorphism groups of the space ... the description of space groups. Z. Kristallogr. 153, 151-179. Fischer, W. & Koch, E. (1983). On the equivalence of ...
[more results from section 3.5.1 in volume A]
Normalizers of space groups and their use in crystallography
International Tables for Crystallography (2016). Vol. A, ch. 3.5, pp. 826-851 [ doi:10.1107/97809553602060000933 ]
... sphere are tabulated. 3.5.1. Introduction and definitions E. Koch, a W. Fischer a andU. Müller b 3.5.1.1. Introduction | | The mathematical concept ... these problems and clarifies the common background (for references, see Fischer & Koch, 1983). 3.5.1.2. Definitions | | Any pair, consisting of ...
Weissenberg complexes
International Tables for Crystallography (2016). Vol. A, Section 3.4.4.7, p. 824 [ doi:10.1107/97809553602060000932 ]
Weissenberg complexes 3.4.4.7. Weissenberg complexes In general, each lattice complex involves point configurations that cannot be related to any crystal structure because the shortest distances between the atoms in a corresponding arrangement would become too small. Only the 67 Weissenberg complexes (cf. Section 3.4.1.5.2) form an exception from this rule. Assuming ...
[more results from section 3.4.4 in volume A]
Assignment of Wyckoff positions to Wyckoff sets and to lattice complexes
International Tables for Crystallography (2016). Vol. A, Section 3.4.3.2, p. 800 [ doi:10.1107/97809553602060000932 ]
... the same Wyckoff set (cf. Sections 1.4.4.3 and 3.4.1.2; Koch & Fischer, 1975), the reference symbol is given only once (e.g. Wyckoff ... s 2 t 4 u m.. * P2y2z 4 v 4 w .m. P2x2z 4 x 4 y ..m P2x2y 4 z ... b .32 4 c 6 d 222.. 6 e 2.22 W 6 f 8 g .3. ..2 I4xxx 12 h ...
[more results from section 3.4.3 in volume A]
Comparison of the concepts of lattice complexes and orbit types
International Tables for Crystallography (2016). Vol. A, Section 3.4.2.2, pp. 796-798 [ doi:10.1107/97809553602060000932 ]
... and crystallographic orbits used for the classifications (cf. also Koch & Fischer, 1985). The concept of orbit types is entirely based ... space groups. Z. Kristallogr. Supplement issue No. 1. Koch, E. & Fischer, W. (1985). Lattice complexes and limiting complexes versus orbit ...
[more results from section 3.4.2 in volume A]
Weissenberg complexes
International Tables for Crystallography (2016). Vol. A, Section 3.4.1.5.2, pp. 795-796 [ doi:10.1107/97809553602060000932 ]
... 1925)]. These lattice complexes were called Weissenberg complexes by Fischer et al. (1973). The 36 invariant lattice complexes are ... plane groups, namely the univariant rectangular complex p2mg c. References Fischer, W., Burzlaff, H., Hellner, E. & Donnay, J. D. H. (1973) ...
[more results from section 3.4.1 in volume A]
Normalizers of point groups
International Tables for Crystallography (2016). Vol. A, Section 3.5.4, p. 851 [ doi:10.1107/97809553602060000933 ]
Normalizers of point groups 3.5.4. Normalizers of point groups Normalizers with respect to the Euclidean or affine group may be defined for any group of isometries (cf. Gubler, 1982a,b). For a point group, however, it seems inadequate to use a supergroup that contains transformations that do not map a ...
International Tables for Crystallography (2016). Vol. A, ch. 3.4, pp. 792-825 [ doi:10.1107/97809553602060000932 ]
... definition used in this chapter was proposed later still by Fischer & Koch (1974a) [cf. also Koch & Fischer (1978a)]. An alternative definition was given by Zimmermann & Burzlaff ... space groups belong to different types. The terms `point configuration' (Fischer & Koch, 1974a) and `crystallographic orbit' (Matsumoto & Wondratschek, 1979) have ...
Reduction of the parameter regions to be considered for geometrical studies of point configurations
International Tables for Crystallography (2016). Vol. A, Section 3.5.3.5, p. 850 [ doi:10.1107/97809553602060000933 ]
... Dirichlet domains etc.), the Euclidean normalizers (cf. e.g. Laves, 1931; Fischer, 1971, 1991; Koch, 1984a) as well as the affine normalizers (cf. Fischer, 1968) of the space groups allow a further reduction of ... Fig. 3.5.2.1) by means of the affine normalizer . References Fischer, W. (1968). Kreispackungsbedingungen in der Ebene. Acta Cryst. ...
[more results from section 3.5.3 in volume A]
Affine normalizers of plane groups and space groups
International Tables for Crystallography (2016). Vol. A, Section 3.5.2.2, pp. 830-838 [ doi:10.1107/97809553602060000933 ]
Affine normalizers of plane groups and space groups 3.5.2.2. Affine normalizers of plane groups and space groups The affine normalizer of a space (plane) group either is a true supergroup of its Euclidean normalizer , or both normalizers coincide: As any translation is an isometry, each translation belonging to also belongs to ...
[more results from section 3.5.2 in volume A]
Definitions
International Tables for Crystallography (2016). Vol. A, Section 3.5.1.2, pp. 826-827 [ doi:10.1107/97809553602060000933 ]
... been tabulated in more detail by Gubler (1982a,b) and Fischer & Koch (1983). The Euclidean normalizers of triclinic and monoclinic ... Wyckoff sets and the definition of lattice complexes by Koch & Fischer (1975), even though there the automorphism groups of the space ... the description of space groups. Z. Kristallogr. 153, 151-179. Fischer, W. & Koch, E. (1983). On the equivalence of ...
[more results from section 3.5.1 in volume A]
Normalizers of space groups and their use in crystallography
International Tables for Crystallography (2016). Vol. A, ch. 3.5, pp. 826-851 [ doi:10.1107/97809553602060000933 ]
... sphere are tabulated. 3.5.1. Introduction and definitions E. Koch, a W. Fischer a andU. Müller b 3.5.1.1. Introduction | | The mathematical concept ... these problems and clarifies the common background (for references, see Fischer & Koch, 1983). 3.5.1.2. Definitions | | Any pair, consisting of ...
Weissenberg complexes
International Tables for Crystallography (2016). Vol. A, Section 3.4.4.7, p. 824 [ doi:10.1107/97809553602060000932 ]
Weissenberg complexes 3.4.4.7. Weissenberg complexes In general, each lattice complex involves point configurations that cannot be related to any crystal structure because the shortest distances between the atoms in a corresponding arrangement would become too small. Only the 67 Weissenberg complexes (cf. Section 3.4.1.5.2) form an exception from this rule. Assuming ...
[more results from section 3.4.4 in volume A]
Assignment of Wyckoff positions to Wyckoff sets and to lattice complexes
International Tables for Crystallography (2016). Vol. A, Section 3.4.3.2, p. 800 [ doi:10.1107/97809553602060000932 ]
... the same Wyckoff set (cf. Sections 1.4.4.3 and 3.4.1.2; Koch & Fischer, 1975), the reference symbol is given only once (e.g. Wyckoff ... s 2 t 4 u m.. * P2y2z 4 v 4 w .m. P2x2z 4 x 4 y ..m P2x2y 4 z ... b .32 4 c 6 d 222.. 6 e 2.22 W 6 f 8 g .3. ..2 I4xxx 12 h ...
[more results from section 3.4.3 in volume A]
Comparison of the concepts of lattice complexes and orbit types
International Tables for Crystallography (2016). Vol. A, Section 3.4.2.2, pp. 796-798 [ doi:10.1107/97809553602060000932 ]
... and crystallographic orbits used for the classifications (cf. also Koch & Fischer, 1985). The concept of orbit types is entirely based ... space groups. Z. Kristallogr. Supplement issue No. 1. Koch, E. & Fischer, W. (1985). Lattice complexes and limiting complexes versus orbit ...
[more results from section 3.4.2 in volume A]
Weissenberg complexes
International Tables for Crystallography (2016). Vol. A, Section 3.4.1.5.2, pp. 795-796 [ doi:10.1107/97809553602060000932 ]
... 1925)]. These lattice complexes were called Weissenberg complexes by Fischer et al. (1973). The 36 invariant lattice complexes are ... plane groups, namely the univariant rectangular complex p2mg c. References Fischer, W., Burzlaff, H., Hellner, E. & Donnay, J. D. H. (1973) ...
[more results from section 3.4.1 in volume A]
Normalizers of point groups
International Tables for Crystallography (2016). Vol. A, Section 3.5.4, p. 851 [ doi:10.1107/97809553602060000933 ]
Normalizers of point groups 3.5.4. Normalizers of point groups Normalizers with respect to the Euclidean or affine group may be defined for any group of isometries (cf. Gubler, 1982a,b). For a point group, however, it seems inadequate to use a supergroup that contains transformations that do not map a ...
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