The reactions of a flexible ligand hexakis(3-pyridyloxy)cyclotriphosphazene (HPCP) with a variety of silver(I) salts (AgX; X = NO3(-), PF6(-), ClO4(-), CH3PhSO3(-), BF4(-) and CF3SO3(-)) afforded six silver(I) coordination polymers, namely {[Ag2(HPCP)]·(NO3)2·H2O}n (1), {[Ag2(HPCP)(CH3CN)]·(PF6)2}n (2), {[Ag2(HPCP)(CH3CN)]·(ClO4)2}n (3), [Ag3(HPCP)(CH3PhSO3)3]n (4), [Ag2(HPCP)(CH3CN)(BF4)2]n (5) and {[Ag(HPCP)]·(CF3SO3)}n (6). All of the isolated crystalline compounds were structurally determined by X-ray crystallography. Changing the counteranions in the reactions, which were conducted under similar conditions of M/L ratio (1:1), temperature and solvent, resulted in structures with different types of topologies. In complexes (1)-(6), the ligand HPCP shows different coordination modes with Ag(I) ions giving two-dimensional layered structures and three-dimensional frameworks with different topologies. Complex (1) displays a new three-dimensional framework adopting a (3,3,6)-connected 3-nodal net with point symbol {4.6(2)}2{4(2).6(10).8(3)}. Complexes (2) and (3) are isomorphous and have a two-dimensional layered structure showing the same 3,6L60 topology with point symbol {4.2(6)}2{4(8).6(6).8}. Complex (4) is a two-dimensional structure incorporating short Ag...Ag argentophilic interactions and has a uninodal 4-connected sql/Shubnikov tetragonal plane net with {4(4).6(2)} topology. Complex (5) exhibits a novel three-dimensional framework and more suprisingly contains twofold interpenetrated honeycomb-like networks, in which the single net has a trinodal (2,3,5)-connected 3-nodal net with point symbol {6(3).8(6).12}{6(3)}{8}. Complex (6) crystallizes in a trigonal crystal system with the space group R\bar 3 and possesses a three-dimensional polymeric structure showing a binodal (4,6)-connected fsh net with the point symbol (4(3).6(3))2.(4(6).6(6).8(3)). The effect of the counteranions on the formation of coordination polymers is discussed in this study.