Patterns formed in dielectric barrier discharge is a typical nonlinear self-organization phenomenon. Research on the patterns helps elucidate the formation and evolution mechanisms of spatiotemporal structures in non-equilibrium systems, while also holding potential application value in fields such as material processing and plasma chemical engineering. A honeycomb superlattice pattern with an alternately-stretched honeycomb frame is observed in dielectric barrier discharge with a rectangular modulated gas gap for the first time and is studied both experimentally and theoretically. As the applied voltage increases, the pattern evolves from a hexagonal superlattice pattern with D_6h symmetry to a quasi honeycomb superlattice pattern with D_2h symmetry. Experimentally, the spatiotemporal structures of these two patterns are measured using an intensified charge coupled device (ICCD) and two photomultiplier tubes (PMTs). It is found that the hexagonal sublattice in the honeycomb superlattice pattern is divided into two sublattices, including a large stripe sublattice and a small stripe lattice. Additionally, the honeycomb frame sublattice is alternately-stretched. Discharges occur during both the rising and falling edges of the applied voltage. Through the estimation of the wall charge quantities of the two types of honeycomb frames and the analysis of the influence of boundaries on pattern formation, it is found that the quasi honeycomb superlattice pattern emerges as a self-organized structure under the influence of gas gap symmetry. Theoretically, the Poisson equation is numerically solved using COMSOL Multiphysics to simulate the electric field of the alternately-stretched honeycomb frame before and after discharge during the rising phase of the applied voltage. The result well explains the experimental phenomenon and provides the formation mechanism of the alternately-stretched honeycomb frame.