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While coverage and geographic forwarding in two- dimensional (2D) wireless sensor networks (WSNs) have been well studied, three-dimensional (3D) WSNs have gained relatively less attention in the literature although real-world applications, such as underwater WSNs, require design in 3D instead of 2D space. Most of geographic forwarding protocols for 2D WSNs, however, assume that all sensors are always awake during forwarding. Such an assumption is not realistic for real-world applications, where sensors are duty-cycled to save energy. In this paper, we propose the first solution to the problem of geographic forwarding in duty-cycled 3D k-covered WSNs, where each point in a 3D field is covered by at least k sensors. First, we analyze the k-coverage problem in 3D WSNs and show that the extension of the analysis in 2D space to 3D space is not straightforward due to the inherent characteristics of the Reuleaux tetrahedron, and propose a new model that guarantees k-coverage for a 3D field. Then, we propose a distributed k-coverage protocol for 3D WSNs. Second, we design a hybrid forwarding protocol for duty-cycled 3D k-covered WSNs, which benefits from the advantages of both deterministic and opportunistic forwarding. Third, we relax some widely used assumptions to promote the use of our joint protocol in real-world scenarios. Finally, we evaluate the performance of our joint protocol. We find a close to perfect match between theoretical and simulation results.