Four coordination polymers, [Co₂(Hnbpdc)₂(nbpdc)(bipy)₂]_n (1), [Co₃(nbpdc)₃(bipy)₃(H₂O)₂]_n·2nH₂O (2), [Co₄(nbpdc)₄(bipy)(H₂O)₄]_n (3), and [Co₂(nbpdc)₂(bpee)_3/2]_n·0.25nH₂O (4) [H₂nbpdc = 2-nitrobiphenyl-4,4′-dicarboxylic acid, bipy = 4,4′-bipyridine and bpee = 1,2-di(4-pyridyl)ethane] have been synthesized by hydrothermal methods and studied by means of X-ray crystallography, topological analyses and magnetic analyses. Compounds 1–3 were synthesized from the same reactants under controlled conditions (pH and ligand ratio). Compounds 1, 2 and 4 contain bis(carboxylate)-bridged dinuclear motifs as secondary building units (SBUs). In 1 and 2 the SBUs are connected into 4⁴ layers by bis(chelating) nbpdc and pairwise bipy linkers. In 1, the layers are pillared into a 3D framework with the pcu topology by Hnbpdc, which is coordinated to one layer and hydrogen-bonded to another layer. In 2, the layers and the linear [Co(bipy)]_n chains intercalated between the layers are connected by nbpdc to produce a 3D framework exhibiting a rarely observed 4,6-connected topology. In 4 the SBUs are connected by nbpdc [bis(chelating) and bis(bridging)] and bpee (single and pairwise) to yield a 3D framework, which defines a new 6-connected net with point symbol (4¹⁰·5²·6³). Notably, this new net and the known hex-6-P6₂22 net represent the first examples of topologically different nets having the same coordination sequences, point and vertex symbols. Compound 3 contains carboxylate- and aqua-bridged tetranuclear motifs as SBUs, which are connected by covalent linkers (nbpdc and bipy) and sextuple O–H⋯O hydrogen bonds to generate a 3D framework, which defines a new 10-connected net with point symbol (4²⁴·5¹²·6⁸·7) (considering only covalent linkers) and a new 12-connected net with point symbol (3¹²·4³⁶·5¹⁷·6) (including also the hydrogen bonds as linkers). Magnetic studies on 1 and 2 demonstrated that the bis(syn–skew-carboxylate) bridges between octahedral Co(II) ions induce ferromagnetic coupling; 4 is peculiar in that octahedral and tetrahedral Co(II) ions are linked by mixed syn–syn and syn–skew carboxylate bridges, which give rise to antiferromagnetic coupling.