In order to increase the system capacity of the 5G mobile communication system, multiple-input multiple-output (MIMO) transmission techniques using a large-scale array over the millimeter-wave band have attracted a great amount of attention. To cope with various types of receivers expected in 5G communications such as user equipment (UE) in small cells, indoor Internet-of-Things (IoT) devices at diverse locations, and drones performing aerial navigation, newer types of antenna arrays require all-directional transmission capability. Existing antenna structures with typical panel arrays, however, have restrictions on their transmission angles in both horizontal and vertical directions. In this paper, we propose to employ three-dimensional (3D) array structures composed of multiple triangular panels for efficient massive MIMO transmission of the next-generation wireless systems. We analyze beamforming characteristics of a uniform triangular array (UTA) suitable for such 3D array configurations and present a basic codebook applicable to UTAs. Using antenna structures with multiple UTA panels, multiuser transmission performance is evaluated to demonstrate the effectiveness of the proposal.