This article summarizes the classes of discrete symmetry groups of the Euclidean plane.
The Schönflies notation is given as infinite limits of 7 dihedral groups.
The yellow regions represent the infinite fundamental domain in each.
The 17 wallpaper groups, with finite fundamental domains, are given by International notation, orbifold notation, and Coxeter notation, classified by the 5 Bravais lattices in the plane: square, oblique (parallelogrammatic), hexagonal (equilateral triangular), rectangular (centered rhombic), and rhombic (centered rectangular).
The related pure reflectional Coxeter group are given with all classes except oblique.