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Subperiodic group

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. 
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