An array of GaN hexagonal pyramids with a side length of 8.0 μm was fabricated by selective epitaxial overgrowth. These microsized pyramids are highly efficient microcavities. Three types of optical resonance modes with mode spacings of 10, 5.0, and 6.0 Å were observed when a single pyramid was pumped optically by an intense ultraviolet laser beam. An optical ray tracing method has been developed for calculating the optical resonance modes inside the pyramid microcavities. It was shown that a single pyramidal cavity can support several different types of optical resonance modes. The calculated mode spacing agrees very well with the observations. The uniqueness and advantages of this class of hexagonal pyramidal microcavities over the other microcavities are discussed. The implications of our finding on the future GaN microcavity light emitters including micro-light-emitting diodes, microcavity lasers, and vertical-cavity-surface emitting lasers are also discussed. © 1999 American Institute of Physics.