List of planar symmetry groups

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This article summarizes the classes of discrete planar symmetry groups:

Point groups

There are two classes of point groups, rotational and reflectional.

Point groups:

Example	Symbols
Example C₅	C_n (n) Cyclic group
Example D₆	D_n (*n) Dihedral group

There are also 7 Frieze groups in the plane which have a fundamental line of symmetry and infinite fundamental domains.

Example pattern	Conway symbols
	(∞∞) (∞x) (∞) (∞∞) (22∞) (2∞) (22∞)

Example
pattern

There are 17 wallpaper groups in the plane with finite fundamental domains.

Rotation

Maximum symmetry per lattice type

Mixed

Other