A method of producing 2D and 3D optical lattices with multi-beam interference by using the pyramid lens and the top-chopped pyramid lens is proposed. The structures of 2D and 3D optical lattices formed by interference of multiple z-axis symmetrically distributed plane waves are numerically simulated and analyzed. The relation between the optical-field distribution and the light beam number is conducted, the interference field tends complicate with the rise of beam numbers, when the arrises of the pyramid are enough and the pyramid can be regarding as an axicon, the interference field becomes a Bassel distribution with a concentric circles structure. In the experiment, the multi-arris pyramid lens and the multi-arris top-chopped pyramid lens are used to generate optical lattices. The experimental results are quite consistent with the simulation results.