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Lattice complexes
International Tables for Crystallography (2016). Vol. A, ch. 3.4, pp. 792-825 [ doi:10.1107/97809553602060000932 ]
... used in this chapter was proposed later still by Fischer & Koch (1974a) [cf. also Koch & Fischer (1978a)]. An alternative definition was given by Zimmermann ... groups belong to different types. The terms `point configuration' (Fischer & Koch, 1974a) and `crystallographic orbit' (Matsumoto & Wondratschek, 1979) have frequently ...
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 ]
... the Euclidean normalizers (cf. e.g. Laves, 1931; Fischer, 1971, 1991; Koch, 1984a) as well as the affine normalizers (cf. Fischer, 1968 ... with two degrees of freedom. Z. Kristallogr. 194, 87-110. Koch, E. (1984a). A geometrical classification of cubic point configurations. ...
[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 ]
... tabulated in more detail by Gubler (1982a,b) and Fischer & Koch (1983). The Euclidean normalizers of triclinic and monoclinic space ... groups with specialized metric of the lattice were determined by Koch & Müller (1990). The affine normalizers of the space ... of Wyckoff sets and the definition of lattice complexes by Koch & Fischer (1975), even though there the automorphism groups 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 ]
... group of the sphere are tabulated. 3.5.1. Introduction and definitions E. Koch, a W. Fischer a andU. Müller b 3.5.1.1. Introduction ... eigensymmetry or their sphere packings and Dirichlet partitions (cf. e.g. Koch, 1984a). In the past, most of these problems ...
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 ]
... to 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. ... a 2 * P 1 b 1 c 1 d 2 e 1 * P2xy 3 pm 1 a .m. p2mm a P[y] 1 b 2 c 1 p2mm e P2x[y] 4 pg 2 a 1 p2mg c ...
[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 ]
... configurations and crystallographic orbits used for the classifications (cf. also Koch & Fischer, 1985). The concept of orbit types is entirely ... of the space groups. Z. Kristallogr. Supplement issue No. 1. Koch, E. & Fischer, W. (1985). Lattice complexes and limiting complexes ...
[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 ]
... distance between any two symmetry-equivalent points belonging to Pmma e cannot become shorter than the minimum of , b and c. ... 1 degrees of freedom in Weissenberg complexfWeissenberg complexf P21/m e 2 1 P2/c e 1 P4/nmm c 1 C2/c e 1 ...
[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 ]
... used in this chapter was proposed later still by Fischer & Koch (1974a) [cf. also Koch & Fischer (1978a)]. An alternative definition was given by Zimmermann ... groups belong to different types. The terms `point configuration' (Fischer & Koch, 1974a) and `crystallographic orbit' (Matsumoto & Wondratschek, 1979) have frequently ...
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 ]
... the Euclidean normalizers (cf. e.g. Laves, 1931; Fischer, 1971, 1991; Koch, 1984a) as well as the affine normalizers (cf. Fischer, 1968 ... with two degrees of freedom. Z. Kristallogr. 194, 87-110. Koch, E. (1984a). A geometrical classification of cubic point configurations. ...
[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 ]
... tabulated in more detail by Gubler (1982a,b) and Fischer & Koch (1983). The Euclidean normalizers of triclinic and monoclinic space ... groups with specialized metric of the lattice were determined by Koch & Müller (1990). The affine normalizers of the space ... of Wyckoff sets and the definition of lattice complexes by Koch & Fischer (1975), even though there the automorphism groups 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 ]
... group of the sphere are tabulated. 3.5.1. Introduction and definitions E. Koch, a W. Fischer a andU. Müller b 3.5.1.1. Introduction ... eigensymmetry or their sphere packings and Dirichlet partitions (cf. e.g. Koch, 1984a). In the past, most of these problems ...
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 ]
... to 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. ... a 2 * P 1 b 1 c 1 d 2 e 1 * P2xy 3 pm 1 a .m. p2mm a P[y] 1 b 2 c 1 p2mm e P2x[y] 4 pg 2 a 1 p2mg c ...
[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 ]
... configurations and crystallographic orbits used for the classifications (cf. also Koch & Fischer, 1985). The concept of orbit types is entirely ... of the space groups. Z. Kristallogr. Supplement issue No. 1. Koch, E. & Fischer, W. (1985). Lattice complexes and limiting complexes ...
[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 ]
... distance between any two symmetry-equivalent points belonging to Pmma e cannot become shorter than the minimum of , b and c. ... 1 degrees of freedom in Weissenberg complexfWeissenberg complexf P21/m e 2 1 P2/c e 1 P4/nmm c 1 C2/c e 1 ...
[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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