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From The Collaborative International Dictionary of English v.0.48:
Acyclic \A*cyc"lic\, a. [Pref. a- not + cyclic.] Not cyclic; not disposed in cycles or whorls; as: (a) (Bot.) Of a flower, having its parts inserted spirally on the receptacle. (b) (Org. Chem.) Having an open-chain structure; aliphatic. [Webster 1913 Suppl.]