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In this paper we show that all 3-manifolds of a family introduced by M. J. Dunwoody are cyclic coverings of lens spaces (possibly S 3 ), branched over genus one 1-bridge knots. As a consequence, we give a positive answer to the Dunwoody conjecture that all the elements of a wide subclass are cyclic coverings of S 3 branched over a knot. Moreover, we show that all branched cyclic coverings of a 2-bridge knot belong to this subclass; this implies that the fundamental group of each branched cyclicdoi:10.1515/form.2001.013 fatcat:26k5wpxo55akjm5mnq33mmgloq