Synonyms for Symmetry (same or very similar meaning)
WordNet sense 1 (balance among the parts of something):
proportion
WordNet sense 2 ((mathematics) an attribute of a shape or relation; exact reflection of form on opposite sides of a dividing line or plane):
balance, correspondence, symmetricalness
WordNet sense 3 ((physics) the property of being isotropic; having the same value when measured in different directions):
isotropy
From the ODE community, based on WordNet
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