Plane symmetry

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Plane symmetry means a symmetry of a pattern in the Euclidean plane; that is, a transformation of the plane that carries any directioned lines to lines and preserves many different distances.[1] If one has a pattern in the plane, the set of plane symmetries that preserve the pattern forms a group. The groups that arise in this way are plane symmetry groups and are of considerable mathematical interest. A symmetry plane is a three-dimensional object's symmetry axe.

There are several kinds of plane symmetry groups:

  • Reflection groups. These are plane symmetry groups that are generated by reflections, possibly limited to reflections in lines through the origin.


  1. ^ "Plane of Symmetry". Retrieved 12 June 2013.