Antonyms for Symmetry (opposite meaning)
WordNet sense 1 (lack of proportion; imbalance among the parts of something):
disproportion
WordNet sense 2 ((mathematics) a lack of symmetry):
asymmetry
WordNet sense 3 (the property of being anisotropic; having a different value when measured in different directions):
anisotropy
From the ODE community, based on WordNet
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