Difference between revisions of "Subperiodic group"
From Online Dictionary of Crystallography
(added distinction between subperiodic and crystallographic subperiodic groups) |
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| − | <font color="blue">Groupe sous-périodique </font> (''Fr'') | + | <font color="blue">Groupe sous-périodique</font> (''Fr''). <font color="red">Subperiodische Gruppe</font> (''Ge''). <font color="black">Gruppo subperiodico</font> (''It''). <font color="purple">亜周期群</font> (''Ja''). <font color="green">Groupo subperiódico</font> (''Sp''). |
| − | 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. |
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| − | + | 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: | |
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| + | *'''frieze groups''': 7 two-dimensional types of groups with one-dimensional translations; | ||
| + | *'''rod groups''': 75 three-dimensional types of groups with one-dimensional translations; | ||
| + | *'''layer groups''': 80 three-dimensional types of groups with two-dimensional translations. | ||
==See also== | ==See also== | ||
| − | ''International Tables | + | *[[subperiodic crystal]] |
| + | *''International Tables for Crystallography, Volume E'' | ||
[[Category:Fundamental crystallography]] | [[Category:Fundamental crystallography]] | ||
Latest revision as of 15:08, 17 February 2021
Groupe sous-périodique (Fr). Subperiodische Gruppe (Ge). Gruppo subperiodico (It). 亜周期群 (Ja). Groupo subperiódico (Sp).
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 types of groups with one-dimensional translations;
- rod groups: 75 three-dimensional types of groups with one-dimensional translations;
- layer groups: 80 three-dimensional types of groups with two-dimensional translations.
See also
- subperiodic crystal
- International Tables for Crystallography, Volume E