Broadcasting is one of the most important operations in the wireless network for disseminating information throughout the entire network. Flooding is a simple mechanism to realize broadcasting, but it has high redundancy of retransmissions, leading to low transmission efficiency. Many broadcast protocols have been proposed for pursuing optimized transmission efficiency for wireless networks hypothetically deployed on the 2-dimesional (2D) plane. In the real world, wireless networks are deployed in the 3D space. In this paper, we derive the upper bound of 3D transmission efficiency and propose a 3D broadcast protocol with optimized transmission efficiency by partitioning the 3D space into multi-layer hexagonal prisms of a hexagon ring pattern in each layer. As we will show, the transmission efficiency of the proposed protocol can reach 1/π, which is better than those of other polyhedron-filling approaches using cubes, hexagon prisms, rhombic dodecahedrons, and truncated octahedrons.