1.30: Crystal pattern
An object in the n-dimensional point space E n is called an n-dimensional crystallographic pattern or, for short, crystal pattern if among its symmetry operations:
- there are n translations, the translation vectors t 1 , ... , t n of which are linearly independent;
- 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 of abstract, in any dimension, which obeys the conditions of periodicity and discreteness expressed above.