Crystal pattern

Motif cristallin (Fr). Motivo cristallino(It). 結晶模様 (Ja).

An object in the n-dimensional point space Eⁿ is called an n-dimensional crystallographic pattern or, for short, crystal pattern if among its symmetry operations:

1. there are n translations, the translation vectors t₁, ... , t_n of which are linearly independent;
2. all translation vectors, except the zero vector 0, have a length of at least d > 0.

When the crystal pattern consists of atoms, it takes the name of crystal structure. The crystal pattern is thus the generalization of a crystal structure to any pattern, concrete or abstract, in any dimension, which obeys the conditions of periodicity and discreteness expressed above.

See also

• Point space
• Noncrystallographic symmetry
• International Tables for Crystallography, Volumes A and A1