A systematic and simple theoretical approach is proposed to analyze true degeneracies and polarized decay patterns of exciton complexes in semiconductor quantum dots. The results provide reliable spectral signatures for efficient symmetry characterization, and predict original features for low C(2 nu) and high C(3 nu) symmetries. Excellent agreement with single quantum dot spectroscopy of real pyramidal InGaAs/AlGaAs quantum dots grown along [111] is demonstrated. The high sensitivity of biexciton quantum states to exact high symmetry can be turned into an efficient uninvasive postgrowth selection procedure for quantum entanglement applications.