Subperiodic group

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 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