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Due to the low-cost design nature of greedy-based routing algorithms, it is considered feasible to adopt this type of schemes within the three-dimensional (3D) wireless sensor networks. In the existing research work, the unreachability problem (i.e., the so-called void problem) resulting from the greedy routing algorithms has not been fully resolved, especially under the 3D environment. In this letter, a three-dimensional greedy anti-void routing (3D-GAR) protocol is proposed to solve the 3D void problem by exploiting the boundary finding technique for the unit ball graph (UBG). The proposed 3D rolling-ball UBG boundary traversal (3D-RUT) scheme is employed to guarantee the delivery of packets from the source to the destination node. The correctness proofs, protocol implementation, and performance evaluation for the proposed 3D-GAR protocol are also given in this letter.