Generating space-filling arrangements of most discrete polyhedra nanostructures of the same shape is not possible. However, if the appropriate individual building blocks are selected (e.g., cubes), or multiple shapes of the appropriate dimensions are matched (e.g., octahedra and tetrahedra) and their pairing interactions are subsequently forced, space-filled architectures may be possible. With flexible molecular ligands (polyethylene glycol-modified DNA), the shape of a polyhedral nanoparticle can be deliberately altered and used to realize geometries that favor space tessellation. In this work, 10 new colloidal crystals were synthesized from DNA-modified nanocrystal building blocks that differed in shapes and sizes, designed to form space-filling architectures with micron-scale dimensions. The insights and capabilities provided by this new strategy substantially expand the scope of colloidal crystals possible and provide an expanded tool kit for researchers interested in designing metamaterials.