Symmetry (geometry)A drawing of a butterfly with bilateral symmetry , with left and right sides as mirror images of each other. A geometric object has symmetry if there is an "operation" or "transformation" (such as an isometry or affine map ) that maps the figure/object onto itself; i.e., it is said that the object has an invariance under the transform.For instance, a circle rotated about its center will have the same shape and size as the original circle—all points before and after the transform would be indistinguishable. A circle is said to be symmetric under rotation or to have rotational symmetry . If the isometry is the reflection of a plane figure , the figure is said to have reflectional symmetry or line symmetry ; moreover, it is possible for a figure/object to have more than one line of symmetry. Te types of symmetries that are possible for a geometric object depend on the set of ...
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