A challenging goal in materials chemistry and physics is spontaneously to form intended superstructures from designed building blocks. In fields such as crystal engineering1 and the design of porous materials2, 3, 4, this typically involves building blocks of organic molecules, sometimes operating together with metallic ions or clusters. The translation of such ideas to nanoparticles and colloidal-sized building blocks would potentially open doors to new materials and new properties5, 6, 7, but the pathways to achieve this goal are still undetermined. Here we show how colloidal spheres can be induced to self-assemble into a complex predetermined colloidal crystal—in this case a colloidal kagome lattice8, 9, 10, 11, 12—through decoration of their surfaces with a simple pattern of hydrophobic domains. The building blocks are simple micrometre-sized spheres with interactions (electrostatic repulsion in the middle, hydrophobic attraction at the poles, which we call ‘triblock Janus’) that are also simple, but the self-assembly of the spheres into an open kagome structure contrasts with previously known close-packed periodic arrangements of spheres13, 14, 15. This open network is of interest for several theoretical reasons8, 9, 10. With a view to possible enhanced functionality, the resulting lattice structure possesses two families of pores, one that is hydrophobic on the rims of the pores and another that is hydrophilic. This strategy of ‘convergent’ self-assembly from easily fabricated16 colloidal building blocks encodes the target supracolloidal architecture, not in localized attractive spots but instead in large redundantly attractive regions, and can be extended to form other supracolloidal networks.