cycle has 14 distinct synonyms spread across 6 of its 11 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.
an interval during which a recurring sequence of events occurs
“the never-ending cycle of the seasons”
a series of poems or songs on the same theme
“Schubert's song cycles”
a periodically repeated sequence of events
“a cycle of reprisal and retaliation”
the unit of frequency; one hertz has a periodic interval of one second (named for Heinrich Rudolph Hertz)
a single complete execution of a periodically repeated phenomenon
“a year constitutes a cycle of the seasons”
a wheeled vehicle that has two wheels and is moved by foot pedals
pass through a cycle
“This machine automatically cycles”
Synonyms, antonyms and the broader and narrower relations for cycle come from Princeton University’s WordNet. Full sources and licences.