Cycloids are particular Petri nets for modelling processes of actions and events, belonging to the fundaments of Petri's general systems theory. Defined by four parameters they provide an algebraic formalism to describe strongly synchronized sequential processes. To further investigate their structure, reduction systems of cycloids are defined in the style of rewriting systems and properties of irreducible cycloids are proved. In particular the synthesis of cycloid parameters from their Petri net structure is derived, leading to an efficient method for a decision procedure for cycloid isomorphism.