Methods, systems, and apparatus, including medium-encoded computer program products, for designing three dimensional lattice structures include, in one aspect, a method including: obtaining a lattice within a 3D lattice design space for a 3D model being created with a 3D modeling program; identifying junctions in the lattice that are potential sources of particle traps at an interface between the 3D lattice design space and a surface present in the 3D model; and removing the potential sources of particle traps by modifying cell space defined between the identified junctions and the surface. In addition, the surface can be a surface of a solid region defined in the 3D model, and the method can include: identifying beams in the lattice having junctions lying on the surface; and extending each of the identified beams by a length amount to cause overlap between the identified beams and the solid region.