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.
The American Heritage Dictionary
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.
Michael Field and Martin Golubitsky.
Symmetry In Chaos.