Controlling the in-plane symmetry of wide-bandgap semiconductor quantum dots (QDs) is essential for room temperature quantum photonic applications using polarization entangled photon pairs. Herein, we report the formation of 3-fold symmetric group III-nitride QDs at the apex of a triangular pyramid via a self-limited growth mechanism. We employed the in-plane rotational symmetry of the c-plane of a Wurtzite crystal and the large built-in piezoelectric field to reduce fine-structure splitting. The QDs exhibit emission that is distinguishable from that of sidewall quantum wells, and the biexciton-exciton cascade possesses a single-photon nature. We observed the relatively low optical polarization anisotropy and small fine structure splitting under the measurement limit (270 mu eV) with the 3-fold symmetric QD. In contrast with current strategies that consider group III-nitride QDs as strongly polarized single-photon emitters, Our approach for controlling the QD symmetry provides a new perspective on such QDs, as polarization-entangled photon pairs.