Two related CoII5-aminoisophthalate coordination frameworks [Co5(μ3−OH)2(5-NH2-bdc)4(H2O)2]·7.5H2O (1, 5-NH2-bdc = 5-aminoisophthalate) and [Co5(μ3−OH)2(5-NH2-bdc)4(bpy)0.5(H2O)]·3H2O (2, bpy = 4,4′-bipyridine) based on [Co5(μ3−OH)2] clusters have been synthesized by hydrothermal reaction, structurally described, as well as properties characterized, that have unusual 3D networks with high connectivity (3,12) and (3,13)-connected, respectively. Notably, the unique (3,13)-connected framework is constructed from the (3,12)-connected network analogue and 4,4′-bipyridyl spacer. Magnetic studies show that a dominant antiferromagnetic coupling between Co(II) ions, and the generation of relatively effective noncompensated moments at very low temperature, mainly arises from the cooperative magnetic effect of the intercluster arrangement in the Td−SP-3Ohmixed-geometry-based pentamer. [ABSTRACT FROM AUTHOR]