symmetry has 5 distinct synonyms spread across 3 of its 3 senses. Each sense below keeps its own list, because a synonym belongs to a meaning and not to a word: swapping one sense's substitute into another sense's sentence is how a thesaurus makes writing worse. Its one recorded opposite is asymmetry.
Counts are distinct word forms across every sense. A synonym that appears under three senses is counted once here and shown three times below, under each sense it belongs to.
(mathematics) an attribute of a shape or relation; exact reflection of form on opposite sides of a dividing line or plane
Synonyms, antonyms and the broader and narrower relations for symmetry come from Princeton University’s WordNet. Full sources and licences.