Real Dictionary

symmetry
uncountable noun: Symmetry in a relationship or agreement is the fact of both sides giving and receiving an equal amount.
variable noun: Something that has symmetry is symmetrical in shape, design, or structure.
variable noun: You can refer to symmetry between countries, institutions, or situations if you think that there is a close similarity between them.

symmetry in American English
similarity of form or arrangement on either side of a dividing line or plane; correspondence of opposite parts in size, shape, and position; condition of being symmetrical
noun: the correspondence in size, form, and arrangement of parts on opposite sides of a plane, line, or point; regularity of form or arrangement in terms of like, reciprocal, or corresponding parts

symmetry in British English
noun: similarity, correspondence, or balance among systems or parts of a system