This paper presents a new type of joints derived from a historic wooden puzzles. A rule-based computational grammar for generating the joints is developed based on the relationship between the three-dimensional shape and its two-dimensional “net”. The rhombic polyhedra family, cube, rhombic dodecahedron, and rhombic triacontahedron are fully explored in the paper as they are the central part of the joints and is enclosed by all the elements around. This paper also presents lattices derived from these joints, and provide structure analysis to compare the structural performance of these lattices. The non-orthogonal lattices provide new way of looking at lattice structures and also provide new challenges for designing assembly techniques for both human, robots, and drones.