Difference between revisions of "Subperiodic group"
From Online Dictionary of Crystallography
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| − | <font color="blue">Groupe sous-périodique</font> (''Fr''). <font color="black">Gruppo subperiodico</font> (''It''). <font color="purple">亜周期群</font> (''Ja'') | + | <font color="blue">Groupe sous-périodique</font> (''Fr''). <font color="black">Gruppo subperiodico</font> (''It''). <font color="purple">亜周期群</font> (''Ja''). |
A '''subperiodic group''' is a [[group]] of [[Euclidean mapping]]s such that its translations form a [[lattice]] in a proper subspace of the space on which it acts. | A '''subperiodic group''' is a [[group]] of [[Euclidean mapping]]s such that its translations form a [[lattice]] in a proper subspace of the space on which it acts. | ||
| − | A '''crystallographic subperiodic group''' in n-dimensional space is a subperiodic group for which the group of linear parts is a crystallographic [[point group]] of n-dimensional space. The crystallographic subperiodic groups in two and three-dimensional space are classified in: | + | A '''crystallographic subperiodic group''' in ''n''-dimensional space is a subperiodic group for which the group of linear parts is a crystallographic [[point group]] of ''n''-dimensional space. The crystallographic subperiodic groups in two and three-dimensional space are classified in: |
*'''frieze groups''': 7 two-dimensional groups with one-dimensional translations; | *'''frieze groups''': 7 two-dimensional groups with one-dimensional translations; | ||
*'''rod groups''': 75 three-dimensional groups with one-dimensional translations; | *'''rod groups''': 75 three-dimensional groups with one-dimensional translations; | ||
*'''layer groups''': 80 three-dimensional groups with two-dimensional translations. | *'''layer groups''': 80 three-dimensional groups with two-dimensional translations. | ||
| − | |||
==See also== | ==See also== | ||
| − | *International Tables | + | *''International Tables for Crystallography, Volume E'' |
[[Category:Fundamental crystallography]] | [[Category:Fundamental crystallography]] | ||
Revision as of 11:31, 17 May 2017
Groupe sous-périodique (Fr). Gruppo subperiodico (It). 亜周期群 (Ja).
A subperiodic group is a group of Euclidean mappings such that its translations form a lattice in a proper subspace of the space on which it acts.
A crystallographic subperiodic group in n-dimensional space is a subperiodic group for which the group of linear parts is a crystallographic point group of n-dimensional space. The crystallographic subperiodic groups in two and three-dimensional space are classified in:
- frieze groups: 7 two-dimensional groups with one-dimensional translations;
- rod groups: 75 three-dimensional groups with one-dimensional translations;
- layer groups: 80 three-dimensional groups with two-dimensional translations.
See also
- International Tables for Crystallography, Volume E