Symmetry

A symmetry is a transformation of an object or system that leaves some of its essential structure unchanged. In geometry, for example, a figure may have rotational, reflective, or translational symmetry if it coincides with itself after being rotated, reflected, or shifted. More generally, symmetry expresses the idea that certain changes do not affect the properties considered important: a physical law may remain unchanged under a change of position or orientation, while an algebraic structure may be preserved by particular transformations of its elements.

Remarks

Mathematically, symmetries are often studied through group theory, which describe how symmetry transformations can be combined and inverted.