Self-assembling colloidal particles in the cubic diamond crystal structure could potentially be used to make materials with a photonic bandgap 1-3. Such materials are beneficial because they suppress spontaneous emission of light 1 and are valued for their applications as optical waveguides, filters and laser resonators 4 , for improving light-harvesting technologies 5-7 and for other applications 4,8. Cubic diamond is preferred for these applications over more easily self-assembled structures, such as face-centred-cubic structures 9,10 , because diamond has a much wider bandgap and is less sensitive to imperfections 11,12. In addition, the bandgap in diamond crystals appears at a refractive index contrast of about 2, which means that a photonic bandgap could be achieved using known materials at optical frequencies; this does not seem to be possible for face-centred-cubic crystals 3,13. However, self-assembly of colloidal diamond is challenging. Because particles in a diamond lattice are tetrahedrally coordinated, one approach has been to self-assemble spherical particles with tetrahedral sticky patches 14-16. But this approach lacks a mechanism to ensure that the patchy spheres select the staggered orientation of tetrahedral bonds on nearest-neighbour particles, which is required for cubic diamond 15,17. Here we show that by using partially compressed tetrahedral clusters with retracted sticky patches, colloidal cubic diamond can be self-assembled using patch-patch adhesion in combination with a steric interlock mechanism that selects the required staggered bond orientation. Photonic bandstructure calculations reveal that the resulting lattices (direct and inverse) have promising optical properties, including a wide and complete photonic bandgap. The colloidal particles in the self-assembled cubic diamond structure are highly constrained and mechanically stable, which makes it possible to dry the suspension and retain the diamond structure. This makes these structures suitable templates for forming high-dielectric-contrast photonic crystals with cubic diamond symmetry.