http://dbpedia.org:8891/sparql?query=define%20sql%3Adescribe-mode%20%22CBD%22%20%20DESCRIBE%20%3Chttp%3A%2F%2Fdbpedia.org%2Fresource%2FPlane_symmetry%3E&output=application%2Fatom%2Bxml2021-05-12T12:56:49.897641ZOData Service and Descriptor Documenthttp://dbpedia.org/resource/Plane_symmetry2021-05-12T12:56:49.897641ZA plane symmetry is 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. 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:A plane symmetry is 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. 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.
* Rotation groups. These groups consist of rotations around a point.
* Translation groups.
* Symmetries of geometrical figures. Some of these are reflection groups, e.g., the group of symmetries of the square or the rectangle. The symmetry group of a swastika or any similar figure without an axis of symmetry is a rotation group.912033992Plane symmetry40393301368