A novel series of two zirconium- and one indium-based metal-organic frameworks (MOFs), namely, MOF-892, MOF-893, and MOF-894, constructed from the hexatopic linker, 1',2',3',4',5',6'-hexakis(4-carboxyphenyl)benzene, were synthesized and fully characterized. MOF-892 and MOF-893 are two new exemplars of materials with topologies previously unseen in the important family of zirconium MOFs. MOF-892, MOF-893, and MOF-894 exhibit efficient heterogeneous catalytic activity for the cycloaddition of CO, resulting in a cyclic organic carbonate formation with high conversion, selectivity, and yield under mild conditions (1 atm CO, 80 °C, and solvent-free). Because of the structural features provided by their building units, MOF-892 and MOF-893 are replete with accessible Lewis and Brønsted acid sites located at the metal clusters and the non-coordinating carboxylic groups of the linkers, respectively, which is found to promote the catalytic CO cycloaddition reaction. As a proof-of-concept, MOF-892 exhibits high catalytic activity in the one-pot synthesis of styrene carbonate from styrene and CO without preliminary synthesis and isolation of styrene oxide.