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cool one's heels has 1 distinct synonym spread across 1 of its 1 sense. Each sense below keeps its own list, because a synonym belongs to a meaning and not to a word: swapping one sense's substitute into another sense's sentence is how a thesaurus makes writing worse. WordNet records no antonym for it — antonymy is a relation between word forms rather than concepts, so it is deliberately sparse.
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.
wait or pass the time aimlessly or futilely; be kept waiting
“She kicked her heels for hours at the gate of the Embassy”
Synonyms, antonyms and the broader and narrower relations for cool one's heels come from Princeton University’s WordNet. Full sources and licences.