We propose and realize the photonic quasicrystal (PQC) single-cell resonator based on a InP-InGaAsP freestanding slab. A well-defined hexapole-like localized state following a C-6v symmetry is identified from the PQC single-cell resonator. In this type of hexapole mode, the electromagnetic energy is strongly concentrated on the dielectric region, in contrast to that in a triangular lattice photonic crystal. By tailoring the structural parameters, the hexapole mode shows a maximum theoretical quality factor of similar to20 000. The PQC single-cell resonator lases in a single hexapole mode with a threshold of similar to0.6 mW at room temperature. (C) 2005 American Institute of Physics. [DOI: 10.1063/1.1852716]