Geometry-Programmed Connectivity Enables Predictive Assembly of Diamond-Family Colloidal Crystals

The predictive assembly of open colloidal crystals requires encoding specific connectivity rules into building blocks that are otherwise isotropic and lack inherent directionality. Here we introduce a geometry-programmed connectivity strategy in which spatial confinement, rather than surface patterning or lattice templating, programs not only particle coordination but also the accessible bonding arrangement that governs network connectivity. We implement this concept using tetrahedral DNA origami frameworks that confine DNA-functionalized spherical particles and restrict their accessible bonding pathways to four tetrahedrally arranged patches, thereby converting isotropic colloids into effective tetravalent building blocks with geometrically prescribed connectivity. A geometric hard-contact model translates these confinement-defined connectivity rules and the linker-defined interaction range into coordination regimes and lattice symmetry, yielding a predictive phase diagram. Guided by this model, we experimentally realize diamond-family colloidal crystals featuring the coexistence of cubic diamond and double diamond phases, as well as zinc blende and double zinc blende phases. Photonic band-structure calculations predict that the experimentally realized cubic diamond and zinc blende topologies can support complete PBGs in the deep-ultraviolet regime. We thus establish a predictive form of colloidal topological engineering, in which confinement geometry programs local connectivity and selects emergent crystal topology.