Bent dipyridyl bases, 2,5-bis(3-pyridyl)-1,3,4-oxadiazole (3-bpo) and its 4-N-donor analogue 2,5-bis(4-pyridyl)-1,3,4-oxadiazole (4-bpo), were applied to crystallize with trimesic acid (benzene-1,3,5-tricarboxylic acid, H(3)TMA) and pyromellitic acid (benzene-1,2,4,5-tetracarboxylic acid, H(4)BTA), affording new binary molecular cocrystals [(H(3)TMA)(.)(3-bpo)](DMF)-D-. (1), [H(3)TMA)(.)(4-bpo)] (2), [(H(4)BTA)-(3-bpo)](.)2H(2)O (3), and a partly charge-transfer salt [(H(2)BTA)(1/2)(.)(H-4-bpo)(.)(H(4)BTA)(1/2)](H2O)-H-. (4) under general conditions. An unexpected compound 5 (pyromellitic dihydrazide) was obtained during the attempt to attain a cocrystal of 4-bpo and H(4)BTA by hydrothermal synthesis. X-ray single-crystal diffraction studies reveal that supramolecular synthon I [R-2(2)(7)] containing classical O-H center dot center dot center dot N and weak C-H center dot center dot center dot O interactions is again testified to be involved in constructing the binary hydrogen-bonding networks 1-4, in which the heteromeric intermolecular interactions are often utilized as effective synthetic tools to provide a significant portion of the stabilization energy of molecular crystals. In compound 1, 1-D acid/base zigzag chains formed by synthon I are extended to a 2-D layered architecture via additional C-H center dot center dot center dot O interactions, the cavities of which are occupied by guest solvents (N,N-dimethylformamide, DMF). Compound 2 displays fascinating 1-D triple-helical motifs via synthon I (formation of the single strand helix) and C-H center dot center dot center dot O interactions, which are further expanded to a 3-D supramolecular array by multiple hydrogen bonds. Self-recognition via hydrogen bonding has been evidently embodied in this unique supramolecular system. In compounds 3 and 4, water moieties are present in both resultant assemblies and play different roles in the formation of 3-D supramolecular networks. For 3, each water molecule acts as a 3-connected node, linking three 1-D acid/base double chains resulting from the combination of synthon I and C-H center dot center dot center dot N bonds, to afford a 3-D sandwich network. For 4, water molecules only behave as guests to further stabilize the robust 3-D hydrogen-bonding host framework. Compound 5 has a 2-D sheet structure via a pair of strong head-to-tail N-H center dot center dot center dot O interactions. The thermal stability of cocrystals 1-4 has been investigated by thermogravimetric analysis of mass loss.