Subperiodic group

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Groupe sous-périodique (Fr); 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 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