arch has 13 distinct synonyms spread across 4 of its 7 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 curved shape in the vertical plane that spans an opening
a curved bony structure supporting or enclosing organs (especially the inner sides of the feet)
(architecture) a masonry construction (usually curved) for spanning an opening and supporting the weight above it
(used of behavior or attitude) characteristic of those who treat others with condescension
naughtily or annoyingly playful
“teasing and worrying with impish laughter”
Synonyms, antonyms and the broader and narrower relations for arch come from Princeton University’s WordNet. Full sources and licences.