Diamond lattices formed by atomic or colloidal elements exhibit remarkable functional properties. However, building such structures via self-assembly has proven to be challenging because of the low packing fraction, sensitivity to bond orientation, and local heterogeneity. We report a strategy for creating a diamond superlattice of nano-objects via self-assembly and demonstrate its experimental realization by assembling two variant diamond lattices, one with and one without atomic analogs. Our approach relies on the association between anisotropic particles with well-defined tetravalent binding topology and isotropic particles. The constrained packing of triangular binding footprints of truncated tetrahedra on a sphere defines a unique three-dimensional lattice. Hence, the diamond self-assembly problem is solved via its mapping onto two-dimensional triangular packing on the surface of isotropic spherical particles.