We describe a modular bond-centric approach to protein nanomaterial design inspired by the rich diversity of chemical structures that can be generated from the small number of atomic valencies and bonding interactions. We design protein building blocks with regular coordination geometries and bonding interactions that enable the assembly of a wide variety of closed and opened nanomaterials using simple geometrical principles. Experimental characterization confirms successful formation of more than twenty multi-component polyhedral protein cages, 2D arrays, and 3D protein lattices, with a high (10-50 %) success rate and electron microscopy data closely matching the corresponding design models. Because of the modularity, individual building blocks can assemble with different partners to generate distinct regular assemblies, resulting in an economy of parts and enabling the construction of reconfigurable systems.