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ellipse 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.
a closed plane curve resulting from the intersection of a circular cone and a plane cutting completely through it
“the sums of the distances from the foci to any point on an ellipse is constant”
Synonyms, antonyms and the broader and narrower relations for ellipse come from Princeton University’s WordNet. Full sources and licences.