In our effect to tune the Co(II) coordination polymer architectures, three position isomers 1,2-, 1,3-, 1,4-bis(1,2,4-triazol-1-ylmethyl)benzene and rigid 5-nitroisophthalate were used to assembly Co (II) coordination polymers [Co(obtz)(NO2-1,3-bdc)](n), (1), [Co(mbtz)(NO2-1,3-bdc)(CH3OH)](n) (2), and [Co(bbtz)-(NO2-1,3-bdc)](n)(H2O)](n) (3). 1 is comprised of undulated two-dimensional (2D) (4,4) networks. Two identical undulated layers are parallel interpenetrated to each other to give a (2D -> 2D) polycatenated 2D network. The adjacent polycatenated 2D layers parallel polythreaded to form a unique 3D network. 1 is an unusual 2D -> 3D polythreaded framework based on the polycatenated 2D layers. 2 shows the double-layer structure through the hydrogen bonds and pi center dot center dot center dot pi stacking interactions based on the undulated 2D (4,4) network. A 3D supramolecular network is constructed through the pi center dot center dot center dot pi stacking interactions interdouble layers. 3 exhibits a 3-fold interpenetrating 4-connected 6(5).8-CdSO4 3D network. The powder X-ray diffraction, thermal stabilities, and UV-vis spectroscopy of 1, 2,, and 3 were investigated.