Symmetry is an intrinsic characteristic of an object that means the object remains unchanged after a symmetry operation is performed on it. Group theory is the area of mathematics that is concerned with the systematic study and formalization of symmetry. A symmetry operation is a mathematical transformation that, when performed on a symmetric object, produces an object that is identical to the original object. Symmetry operations are defined relative to a given point, center of symmetry, line, axis of symmetry, or plane, plane of symmetry, and when performed on symmetric objects preserve distances, angles, sizes, and shapes. In mathematics there are several kinds of symmetries but plane symmetry, those whose operations take place in a plane on two-dimensional figures, and spatial symmetry, those whose operations take place in three-dimensional space on solid shapes, are the most common.

Although symmetry is an important conceptual tool of modern science the...