Using the interference of N collimated laser beams, optical lattices with N-fold rotational symmetry are generated over the interface of two semi-infinite dielectric media. The interaction of small dielectric particles with these interference patterns is investigated using Rayleigh approximation. The polarization state of the interfering beams considerably influences the interference patterns and potential landscapes. Therefore, both parallel and perpendicular polarized interfering beams are considered and the corresponding potential profiles are compared and analyzed. We also study how the number of interfering waves, incident and azimuth angles, and initial phases of the incident beams influence optical lattices and potential profiles. It is found that the ring-shaped patterns with good confinement properties can be achieved by increasing the number of incident beams. In addition, by increasing the number of incident beams one can make an optical trap with sharper intensity gradient and deeper potential well, which is an advantage for trapping small Rayleigh particles. The lattices resulting from the interference of N incident waves with different incident angles are also investigated. Furthermore, the effects of changing the azimuth angles between two adjacent incident wave vectors on the intensity patterns are studied. The proposed configuration and the numerical results can find numerous applications in particle arrangement, particle sorting, and the creation of quasicrystals. We believe that interference approaches have many potential capabilities for molding light wavefronts and creating multiple traps with sophisticated patterns.