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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'')
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<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.
  
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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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.
 
  
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*'''frieze groups''': 7 two-dimensional types of groups with one-dimensional translations;
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*'''rod groups''': 75 three-dimensional types of groups with one-dimensional translations;
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*'''layer groups''': 80 three-dimensional types of groups with two-dimensional translations.
  
 
==See also==
 
==See also==
*International Tables of Crystallography, Volume E
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*[[subperiodic crystal]]
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*''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