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dbr:Plane_symmetry
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Plane symmetry
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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:
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wikipedia-en:Plane_symmetry
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dbc:Euclidean_geometry
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912033992
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dbr:Group_(mathematics) dbr:Plane_(geometry) dbr:Rotational_symmetry dbr:Reflection_group dbr:Rectangle dbr:Geometric_shape dbc:Euclidean_geometry dbr:Circle_group dbr:Square dbr:Translation_(geometry) dbr:Swastika
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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.
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