WordNet records no synonym and no antonym for damocles. 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.
the Greek courtier to Dionysius the Elder who (according to legend) was condemned to sit under a naked sword that was suspended by a hair in order to demonstrate to him that being a king was not the happy state Damocles had said it was (4th century BC)
Synonyms, antonyms and the broader and narrower relations for damocles come from Princeton University’s WordNet. Full sources and licences.