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Difference between revisions of "Subperiodic group"

From Online Dictionary of Crystallography

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(added distinction between subperiodic and crystallographic subperiodic groups)
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A '''subperiodic group''' is a group possessing translational periodicity in a subspace of the space where the group is acting. Subperiodic groups in two and three-dimensional spaces are classified in:
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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:
  
 
*'''frieze groups''': 7 two-dimensional groups with one-dimensional translations;
 
*'''frieze groups''': 7 two-dimensional groups with one-dimensional translations;

Revision as of 12:59, 1 April 2009

Groupe sous-périodique (Fr); Gruppo subperiodico (It).


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 of Crystallography, Volume E