1: correspondence in size, shape, and position of parts that are on opposite sides of a dividing line or center.

2: an arragement marked by regularity and balanced proportions syn proportion, balance, harmony.

symmetry n. Exact correspondence of form and constituent configuration on opposite sides of a dividing line or plane or about a center or an axis.

Suppose you have an object and pick it up, move it around and set it down. If it is impossible to distinguish between the object in its original and final positions, we say it has a symmetry. ...

Symmetry of a (planar) picture is a motion of the plane that leaves that picture unchanged.

It is not surprising that symmetry plays such a pivotal role in a wide range of human activity, from decorative design and textiles to architecture and advertising logos. [snip] ... symmetry is a great harmonizer and unifier. We frequently portray, obtain, or symbolize, meaning by the use of symmetry. [snip] This process of using symmetry to obtain harmony and unity is also to be found in science. Many of our modern ideas about universe are based, just as those of the Greeks were, on symmetry.