On the basis of the primary carboxyl/pyridyl hydrogen-bonded synthon, 2,5-bis(3-pyridyl)-1,3,4-oxadiazole (3-bpo) and its 4-N-donor isomer 2,5-bis(4-pyridyl)-1,3,4-oxadiazole (4-bpo) were assembled with flexible dicarboxylic acids possessing variable chain lengths to afford a series of organic cocrystalline materials. [Fumaric acid]‚[3-bpo] (1) has a two-dimensional (2-D) layered supramolecular pattern. [Fumaric acid]‚[4-bpo] (2) has linear tapes connected via carboxyl/pyridyl heterosynthons and further creates a three-dimensional (3-D) square net with the CdSO 4 topology combining with other weak interactions. [Suberic acid]‚[3-bpo] (3), obtained in ambient conditions, exhibits a 3-D corrugated network; however, [suberic acid]‚[4-bph] (4), produced unexpectedly by hydrothermal synthesis, displays a 3-D framework expanding from 2-D layers, in which N,N′-bis(4-picolinoyl) hydrazine (4-bph) is generated in situ from the hydrolysis of 4-bpo. [Benzene-1,4-dioxyacetic acid]‚[3-bpo] (5) takes on a nearly planar 2-D sheet, while [benzene-1,4-dioxyacetic acid]‚[4-bpo] (6) presents an unusual bilayered structure. For all binary compounds except 1, the acid-base components are connected by the carboxyl/pyridyl heterosynthon [O-H‚‚‚N and C-H‚‚‚O, R 2 2 ( 7)], which has been well exploited to engineer plenty of ordered crystalline architectures, to generate linear or zigzag tapes. Via subsidiary C-H‚‚‚O and/or N-H‚‚‚O (only for 4) hydrogen bonds between the neighboring tapes, these 1-D arrays are further extended to diverse networks from 2-D to 3-D. The similarities/differences between the hydrogen-bonded motifs of the cocrystals based on the flexible (alkyl) and rigid (aromatic) dicarboxylic acids with the same bent dipyridyl bases are also discussed, which may further enhance the crystal engineering of organic solids.