The syntheses and X-ray structures of three isomeric 1D coordination polymers are reported. The complex [Co(dbm)2(MeOH)2] (1) was used as a precursor in these reactions. The preparation and structure of 1 is also presented; this mononuclear complex is in the cis configuration because this allows the formation of a network of intermolecular hydrogen bonds in the solid state. Reaction of 1 with 2,4,6-tris-(4-pyridyl)-1,3,5-triazine (4ptz) yields the polymers [Co(dbm)2(4ptz)]n.nTHF (2a), [Co(dbm)2(4ptz)]n.0.75nTHF.0.5nEt2O (2b), and [Co(dbm)2(4ptz)]n.3nDMF (2c) in the form of zigzag chains, instead of the expected honeycomb architectures. This is because of the establishment of extended pi-pi stacking throughout these solids, which could not have occurred otherwise. Compounds 2a, 2b, and 2c are solvatomorphs, and formation of either one of them depends on the exact conditions of crystallization, which lead to significant differences in the supramolecular organization of the chains. Bulk magnetic measurements on 2a reveal weak antiferromagnetic exchange within the chains and small ordering throughout the solid that results in the manifestation of the phenomenon of spin canting, whereas for 2c the different supramolecular organization causes the antiferromagnetic exchange not to result in spin canting.