Crystalline nanoparticle arrays and superlattices with well-defined geometries can be synthesized by using appropriate electrostatic, hydrogen-bonding or biological recognition interactions. Although superlattices with many distinct geometries can be produced using these approaches, the library of achievable lattices could be increased by developing a strategy that allows some of the nanoparticles within a binary lattice to be replaced with 'spacer' entities that are constructed to mimic the behaviour of the nanoparticles they replace, even though they do not contain an inorganic core. The inclusion of these spacer entities within a known binary superlattice would effectively delete one set of nanoparticles without affecting the positions of the other set. Here, we show how hollow DNA nanostructures can be used as 'three-dimensional spacers' within nanoparticle superlattices assembled through programmable DNA interactions. We show that this strategy can be used to form superlattices with five distinct symmetries, including one that has never before been observed in any crystalline material.