The structure-directing effects of a series of polymethylimidazolium cations with different numbers of methyl groups as organic structure-directing agents (OSDAs) in the synthesis of aluminophosphate (AlPO4)-based molecular sieves in both fluoride and hydroxide media are investigated. On the one hand, among the OSDAs studied here, the smallest 1,3-dimethylimidazolium and the largest 1,2,3,4,5-pentamethylimidazolium cations were found to direct the synthesis of a new variant of the triclinic chabazite (CHA)-type AlPO4 material, designated AlPO4-34(t)(v), and the one-dimensional small-pore silicoalumino-phosphate (SAPO) molecular sieve STA-6 in hydroxide media, respectively. On the other hand, the intermediate-sized 1,2,3,4-tetramethylimidazolium cation gave SSZ-51, a two-dimensional large-pore SAPO material, in fluoride media. Synchrotron powder X-ray diffraction and Rietveld analyses reveal that as-made AlPO4-34(t)(v) contains penta-coordinated framework Al species connected by hydroxyl groups, as well as tetrahedral framework Al, which contrasts with the distortions arising from the two F- or OH- bridges between octahedral Al atoms in all already known AlPO4-34 materials. The presence of Al-OH-Al linkages in this triclinic AlPO4-34 molecular sieve has been further corroborated by thermal analysis, variable-temperature IR, Al-27 magic-angle spinning NMR, and dispersion-corrected density functional theory calculations.