Plane Crystallographic Patterns

If a repeating pattern admits translations in two or more directions, it is called a two dimensional pattern or planar pattern, and its symmetry group is called a plane crystallographic group.

The seventeen types of planar patterns and their symmetry groups are as follows:



The following flowchart from (*) is a useful tool in identifying the symmetry group of a planar pattern.

Crowe Flow

*Symmetries of Culture: Theory and Practice of Plane Pattern Analysis by Dorothy Washburn and Donald Crowe, University of Washington Press, 1991