Metal-organic polyhedra (MOPs) or frameworks (MOFs) based on Cr 3+ are notoriously difficult to synthesize, especially as crystals large enough to be suitable for characterization of the structure or properties.I ti sn ow shown that the co-existence of In 3+ and Cr 3+ induces arapid crystal growth of large single crystals of heterometallic In-Cr-MOPs with the [M 8 L 12 ]( M=In/Cr,L=dinegative 4,5-imidazole-dicarboxylate) cubane-like structure.W ith ah igh concentration of protons from 12 carboxyl groups decorating every edge of the cube and an extensive H-bonded network between cubes and surrounding H 2 Omolecules,the newly synthesized In-CrMOPs exhibit an exceptionally high proton conductivity (up to 5.8 10 À2 Scm À1 at 22.5 8 8Ca nd 98 %r elative humidity,s ingle crystal).Metal-organic frameworks (MOFs) [1] (or more generally coordination polymers,C Ps [2] )a nd hydrogen-bonded frameworks including recently developed hydrogen-bonded organic frameworks (HOFs) [3] have emerged as an ew promising class of materials that are capable of fast ion conductivity.T heir high crystallinity and open framework architecture,t ogether with tunable compositions and structures,m ake it possible to not only better design materials to optimize ion conduction carriers and pathways,but also better understand conducting behaviors and mechanisms. [4,5] Highly proton-conducting materials are essential in many applications,especially hydrogen fuel cells.F or MOF materials,r ecently reported strategies for enhancing the proton conductivity have focused on increasing the concentration of proton carriers by controlling framework or extra-framework compositions as well as on improving proton mobility by constructing materials with desired H-bonded networks.F or example,K itagawa et al. reported highly proton-conductive zinc oxalate MOFs by maximizing the proton carriers with the simultaneous introduction of adipic acid molecules on the framework and the counter cation (NH 4 ) + in the void space.[6]Another example is PCMOF2 1 = 2 reported by Shimizu et al. [7] which combined trisulfonate and triphosphonate groups and had conductivity over 0.01 Scm À1 . Thed esign strategy for the synthesis of MOFs can vary significantly depending on the intended applications.F or developing better proton conductors,t he conventional strategy targeting extended 1D,2D, or 3D frameworks may not always be desirable.T his is because ah igher dimensional structure generally requires ag reater degree of ligand deprotonation, which necessarily reduces the proton concentration. Forthis reason, we expect that discrete metal-organic polyhedra (MOPs) that can be formed through partial deprotonation of ligands might represent ap romising source of materials capable of improved fast proton conductivity. Thef inite polyhedral structures of MOPs provide an opportunity to decorate the entire surface with organic ligands that carry extra functional groups so that ahigher concentration of proton carriers can be achieved. Moreover,t he extensive hydrogen bonding ...