This article summarizes the classes of discrete planar symmetry groups:
- 1 simple symmetries (reflection)
- 2 infinite set of point groups
- 7 Frieze groups
- 17 wallpaper groups
Contents |
Simple symmetry
Point groups:
| Example | Symbols |
|---|---|
 Example:Kite |
(*) Reflection symmetry |
Point groups
There are two classes of point groups, rotational and reflectional.
Point groups:
| Example | Symbols |
|---|---|
 Example:Flag of Hong Kong C5 |
Cn (n) Cyclic group |
 Example: Snowflake D6 |
Dn (*n) Dihedral group |
Frieze groups
There are also 7 Frieze groups in the plane which have a fundamental line of symmetry and infinite fundamental domains.
| Example pattern |
orbifold notation |
|---|---|
 |
|
Wallpaper groups
There are 17 wallpaper groups in the plane with finite fundamental domains.
Rotation
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Maximum symmetry per lattice type
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Mixed
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Other
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Note: with regard to the number of mirrors p4m is "more symmetry" than p4g, with regard to the size of the fundamental domain it is an "equal amount of symmetry".
See also
External references
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