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In wireless sensor networks, multiple-coverage, in which each point is covered by more than one sensor, is often required to improve detection quality and achieve high fault tolerance. However, finding optimal patterns that achieve multiple-coverage in a plane remains a long-lasting open problem. In this paper, we first derive the optimal deployment density bound for two-covered deployment patterns where Voronoi polygons generated by sensor nodes are congruent. We then propose optimal two-coverage patterns based on the optimal bound. We further extend these patterns by considering the connectivity requirement and design a set of optimal patterns that achieve two-coverage and one-, two-, and three-connectivity. We also study optimal patterns under practical considerations. To our knowledge, our work is the very first that proves the optimality of multiple-covered deployment patterns.