The syntheses and structures of polymeric silver(l)-diphosphine complexes are reported, in which the silver(l) center is surrounded by 1, 2, or 3 phosphorus atoms. When rigid diphosphine ligands are used in combination with weakly coordinating anions, linear polymers are obtained that contain both diphosphine and anion bridges. However, with excess of a diphosphine with a long, flexible, spacer group, a remarkable puckered sheet structure, comprised of fused giant 54-membered rings, is obtained that is a coordination polymer analogue of laminated materials such as micas and clays. The polymeric chain and sheet structures may be considered to be formed by ring-opening polymerization of cyclic precursors.