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Minimal isotypic supergroups and enantiomorphic supergroups of lowest index
International Tables for Crystallography (2010). Vol. E, Section 1.2.15.4, p. 21 [ doi:10.1107/97809553602060000783 ]
Minimal isotypic supergroups and enantiomorphic supergroups of lowest index 1.2.15.4. Minimal isotypic supergroups and enantiomorphic supergroups of lowest index No data are listed for supergroups IIc, because they can be derived directly from the corresponding data of subgroups IIc. Example: G: Rod group (R29) The maximal isotypic subgroup of lowest index ...
[more results from section 1.2.15 in volume E]
Projection of symmetry elements
International Tables for Crystallography (2010). Vol. E, Section 1.2.14.3, p. 19 [ doi:10.1107/97809553602060000783 ]
... atoms. Result: Plane group c1m1 (5) with a' = a and b' = b. Projection along [100]: The frieze group has the basis vector a' = b/2 due to the centred lattice of the layer ...
[more results from section 1.2.14 in volume E]
Reflection conditions
International Tables for Crystallography (2010). Vol. E, Section 1.2.13, p. 17 [ doi:10.1107/97809553602060000783 ]
... h = 2n (001) a/2 a hk: k = 2n (001) b/2 b hk: (001) a/2 + b/2 n 0k: k = 2n (100) b/2 b ...
Oriented site-symmetry symbols
International Tables for Crystallography (2010). Vol. E, Section 1.2.12, pp. 16-17 [ doi:10.1107/97809553602060000783 ]
Oriented site-symmetry symbols 1.2.12. Oriented site-symmetry symbols The third column of each Wyckoff position gives the site symmetry of that position. The site-symmetry group is isomorphic to a proper or improper subgroup of the point group to which the subperiodic group under consideration belongs. Oriented site-symmetry symbols ...
Positions
International Tables for Crystallography (2010). Vol. E, Section 1.2.11, p. 16 [ doi:10.1107/97809553602060000783 ]
Positions 1.2.11. Positions The entries under Positions (more explicitly called Wyckoff positions) consist of the General position (upper block) and the Special positions (blocks below). The columns in each block, from left to right, contain the following information for each Wyckoff position. (i) Multiplicity M of the Wyckoff position. This ...
Generators
International Tables for Crystallography (2010). Vol. E, Section 1.2.10, p. 16 [ doi:10.1107/97809553602060000783 ]
Generators 1.2.10. Generators The line Generators selected states the symmetry operations and their sequence selected to generate all symmetrically equivalent points of the General position from a point with coordinates . The identity operation given by (1) is always selected as the first generator. The generating translations are listed next, t ...
Designation of symmetry operations
International Tables for Crystallography (2010). Vol. E, Section 1.2.9.2, p. 16 [ doi:10.1107/97809553602060000783 ]
... glide reflections a(1/2, 0, 0) [equivalent to] a; b(0, 1/2, 0) [equivalent to] b; c(0, 0, 1/2) [equivalent to] c. Glide reflections ...
[more results from section 1.2.9 in volume E]
Layer groups
International Tables for Crystallography (2010). Vol. E, Section 1.2.8.3, p. 15 [ doi:10.1107/97809553602060000783 ]
... the asymmetric unit for (a) tetragonal/square layer groups and (b) trigonal/hexagonal and hexagonal/hexagonal layer groups. In (b), the coordinates (x, y) of the vertices of the asymmetric ...
[more results from section 1.2.8 in volume E]
Origin
International Tables for Crystallography (2010). Vol. E, Section 1.2.7, p. 14 [ doi:10.1107/97809553602060000783 ]
Origin 1.2.7. Origin The origin has been chosen according to the following conventions: (i) If the subperiodic group is centrosymmetric, then the inversion centre is chosen as the origin. For the three layer groups p4/n (L52), p4/nbm (L62) and p4/nmm (L64), we give descriptions for two origins, at ...
Subperiodic group diagrams
International Tables for Crystallography (2010). Vol. E, Section 1.2.6, pp. 8-14 [ doi:10.1107/97809553602060000783 ]
... settings, i.e. for two ways of assigning the labels a, b, c to the basis vectors of the conventional coordinate system. ... that the basis vectors relabelled in this setting as a, b and c were in the standard setting labelled c, a and b, respectively [cf. Section 2.2.6 of IT A (2005)]. ...
International Tables for Crystallography (2010). Vol. E, Section 1.2.15.4, p. 21 [ doi:10.1107/97809553602060000783 ]
Minimal isotypic supergroups and enantiomorphic supergroups of lowest index 1.2.15.4. Minimal isotypic supergroups and enantiomorphic supergroups of lowest index No data are listed for supergroups IIc, because they can be derived directly from the corresponding data of subgroups IIc. Example: G: Rod group (R29) The maximal isotypic subgroup of lowest index ...
[more results from section 1.2.15 in volume E]
Projection of symmetry elements
International Tables for Crystallography (2010). Vol. E, Section 1.2.14.3, p. 19 [ doi:10.1107/97809553602060000783 ]
... atoms. Result: Plane group c1m1 (5) with a' = a and b' = b. Projection along [100]: The frieze group has the basis vector a' = b/2 due to the centred lattice of the layer ...
[more results from section 1.2.14 in volume E]
Reflection conditions
International Tables for Crystallography (2010). Vol. E, Section 1.2.13, p. 17 [ doi:10.1107/97809553602060000783 ]
... h = 2n (001) a/2 a hk: k = 2n (001) b/2 b hk: (001) a/2 + b/2 n 0k: k = 2n (100) b/2 b ...
Oriented site-symmetry symbols
International Tables for Crystallography (2010). Vol. E, Section 1.2.12, pp. 16-17 [ doi:10.1107/97809553602060000783 ]
Oriented site-symmetry symbols 1.2.12. Oriented site-symmetry symbols The third column of each Wyckoff position gives the site symmetry of that position. The site-symmetry group is isomorphic to a proper or improper subgroup of the point group to which the subperiodic group under consideration belongs. Oriented site-symmetry symbols ...
Positions
International Tables for Crystallography (2010). Vol. E, Section 1.2.11, p. 16 [ doi:10.1107/97809553602060000783 ]
Positions 1.2.11. Positions The entries under Positions (more explicitly called Wyckoff positions) consist of the General position (upper block) and the Special positions (blocks below). The columns in each block, from left to right, contain the following information for each Wyckoff position. (i) Multiplicity M of the Wyckoff position. This ...
Generators
International Tables for Crystallography (2010). Vol. E, Section 1.2.10, p. 16 [ doi:10.1107/97809553602060000783 ]
Generators 1.2.10. Generators The line Generators selected states the symmetry operations and their sequence selected to generate all symmetrically equivalent points of the General position from a point with coordinates . The identity operation given by (1) is always selected as the first generator. The generating translations are listed next, t ...
Designation of symmetry operations
International Tables for Crystallography (2010). Vol. E, Section 1.2.9.2, p. 16 [ doi:10.1107/97809553602060000783 ]
... glide reflections a(1/2, 0, 0) [equivalent to] a; b(0, 1/2, 0) [equivalent to] b; c(0, 0, 1/2) [equivalent to] c. Glide reflections ...
[more results from section 1.2.9 in volume E]
Layer groups
International Tables for Crystallography (2010). Vol. E, Section 1.2.8.3, p. 15 [ doi:10.1107/97809553602060000783 ]
... the asymmetric unit for (a) tetragonal/square layer groups and (b) trigonal/hexagonal and hexagonal/hexagonal layer groups. In (b), the coordinates (x, y) of the vertices of the asymmetric ...
[more results from section 1.2.8 in volume E]
Origin
International Tables for Crystallography (2010). Vol. E, Section 1.2.7, p. 14 [ doi:10.1107/97809553602060000783 ]
Origin 1.2.7. Origin The origin has been chosen according to the following conventions: (i) If the subperiodic group is centrosymmetric, then the inversion centre is chosen as the origin. For the three layer groups p4/n (L52), p4/nbm (L62) and p4/nmm (L64), we give descriptions for two origins, at ...
Subperiodic group diagrams
International Tables for Crystallography (2010). Vol. E, Section 1.2.6, pp. 8-14 [ doi:10.1107/97809553602060000783 ]
... settings, i.e. for two ways of assigning the labels a, b, c to the basis vectors of the conventional coordinate system. ... that the basis vectors relabelled in this setting as a, b and c were in the standard setting labelled c, a and b, respectively [cf. Section 2.2.6 of IT A (2005)]. ...
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