Three-dimensional mesoscale clusters that are formed from nanoparticles spatially arranged in pre-determined positions can be thought of as mesoscale analogues of molecules. These nanoparticle architectures could offer tailored properties due to collective effects, but developing a general platform for fabricating such clusters is a significant challenge. Here, we report a strategy for assembling three-dimensional nanoparticle clusters that uses a molecular frame designed with encoded vertices for particle placement. The frame is a DNA origami octahedron and can be used to fabricate clusters with various symmetries and particle compositions. Cryo-electron microscopy is used to uncover the structure of the DNA frame and to reveal that the nanoparticles are spatially coordinated in the prescribed manner. We show that the DNA frame and one set of nanoparticles can be used to create nanoclusters with different chiroptical activities. We also show that the octahedra can serve as programmable interparticle linkers, allowing one- and two-dimensional arrays to be assembled with designed particle arrangements.