Methods, systems, and apparatus, including medium-encoded computer program products, for designing three dimensional lattice structures include, in one aspect, a method including: creating nodes in a plane normal to an axis in accordance with a spiral, wherein proper subsets of the nodes occur at successive radii positions away from the axis in the plane normal to the axis; repositioning every other one of the proper subsets, from at least a portion of the nodes, in a direction in 3D space along the axis; creating a three dimensional (3D) structure in the 3D space, the 3D structure comprising beams placed between the repositioned and non-repositioned proper subsets; duplicating the 3D structure one or more times to form a lattice in the 3D space; and selecting at least a portion of the lattice for inclusion in a 3D model.