This work investigates the single-photon emissions from self-assembled InGaAs quantum dots that are grown on an apex plane of a GaAs pyramid-like multifaceted structure. The number of QDs on a multifaceted structure is estimated by scanning electron microscopy. Single-exciton emissions from individual quantum dots are examined by micro-photoluminescence and by making photon correlation measurements. This experiment demonstrates the improvement of the single-photon extraction efficiency as quantum dots are grown on a reduced apex plane of a multifaceted structure.