DNA-programmable assembly has been used to deliberately synthesize hundreds of different colloidal crystals spanning dozens of symmetries, but the complexity of the achieved structures has so far been limited to small unit cells. We assembled DNA-modified triangular bipyramids (~250-nanometer long edge, 177-nanometer short edge) into clathrate architectures. Electron microscopy images revealed that at least three different structures form as large single-domain architectures or as multidomain materials. Ordered assemblies, isostructural to clathrates, were identified with the help of molecular simulations and geometric analysis. These structures are the most sophisticated architectures made via programmable assembly, and their formation can be understood based on the shape of the nanoparticle building blocks and mode of DNA functionalization.