For efficient beamforming over entire three-dimensional space using massive arrays, antenna structures in spherical shape can be used for next-generation transceivers. In this paper, we propose the usage of antenna arrays constructed on geodesic spheres for such purposes and analyze the corresponding beamforming performance. In particular, beam patterns generated by geodesic antenna arrays based on icosahedron are evaluated and compared with conventional beam patterns. We also present beamforming vectors for the 12-sector operation of geodesic arrays, which can be applied to practical operation of limited-feedback channel scenarios.