A large fraction of proteins naturally exist as symmetrical homooligomers or homopolymers1. The emergent structural and functional properties of such protein assemblies have inspired extensive efforts in biomolecular design2-5. As synthesized by ribosomes, proteins are inherently asymmetric. Thus, they must acquire multiple surface patches that selectively associate to generate different symmetry elements needed to form higher-order architectures1,6 – a daunting task for protein design. Here we introduce an inorganic chemical approach to address this outstanding problem, whereby multiple modes of protein-protein interactions and symmetry are simultaneously achieved by selective, “one-pot” coordination of soft and hard metal ions. We show that a monomeric protein (protomer) appropriately modified with biologically inspired hydroxamate groups and Zn-binding motifs assembles through concurrent Fe3+ and Zn2+ coordination into discrete dodecameric and hexameric cages. Closely resembling natural polyhedral protein architectures7,8 and unique among designed systems9-13, our artificial cages possess tightly packed shells devoid of large apertures, yet they can assemble and disassemble in response to diverse stimuli owing to their heterobimetallic construction on minimal interprotein-bonding footprints. With stoichiometries ranging from [2 Fe:9 Zn:6 protomer] to [8 Fe:21 Zn:12 protomer], these protein cages represent some of the compositionally most complex protein assemblies–or inorganic coordination complexes–obtained by design.