rem has 4 distinct synonyms spread across 1 of its 2 senses. 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 recurring sleep state during which dreaming occurs; a state of rapidly shifting eye movements during sleep
(roentgen equivalent man) the dosage of ionizing radiation that will cause the same amount of injury to human tissue as 1 roentgen of X-rays
Synonyms, antonyms and the broader and narrower relations for rem come from Princeton University’s WordNet. Full sources and licences.