WordNet records no synonym and no antonym for gordian knot. 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.
any very difficult problem; insoluble in its own terms
an intricate knot tied by Gordius, the king of Phrygia, and cut by the sword of Alexander the Great after he heard that whoever undid it would become ruler of Asia
Synonyms, antonyms and the broader and narrower relations for gordian knot come from Princeton University’s WordNet. Full sources and licences.