List of planar symmetry groups

This article summarizes the classes of discrete symmetry groups of the Euclidean plane. The symmetry groups are named here by three naming schemes: International notation, orbifold notation, and Coxeter notation. There are three kinds of symmetry groups of the plane:

• 2 families of rosette groups – 2D point groups
• 7 frieze groups – 2D line groups
• 17 wallpaper groups – 2D space groups.