  We report condensation of hexagonal whispering gallery modes (WGM) at room
temperature in ZnO microwires that embody nearly perfect polygonal whispering
gallery microresonators. The condensate regime is achieved in the UV spectral
range only at energies below the first longitudinal optical (LO) phonon replica
of the free ZnO A-exciton transition and at non-zero wave vectors. We
demonstrate that the multimodality of the WGM system and the high population of
free excitons and phonons with various momenta strongly enhance the probability
of an interaction of quasiparticles of the cavity exciton-photon system with LO
phonons. We further examine the far-field mode pattern of lasing WGM and
demonstrate their spatial coherence.
