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WordNet records no synonym and no antonym for bigamy. It is the only member of each of its synsets, which is common for technical, taxonomic and single-sense vocabulary — there is no other English word that means the same thing. The broader and narrower terms below are the useful relations in that case.
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.
the state of having two spouses at the same time
the offense of marrying someone while you have a living spouse from whom no valid divorce has occurred
Synonyms, antonyms and the broader and narrower relations for bigamy come from Princeton University’s WordNet. Full sources and licences.