WordNet records no synonym and no antonym for homograph. It is the only member of its synset, 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.
two words are homographs if they are spelled the same way but differ in meaning (e.g. fair)
Synonyms, antonyms and the broader and narrower relations for homograph come from Princeton University’s WordNet. Full sources and licences.