We present results on the polarization-resolved photoluminescence emitted from InGaAs/AlGaAs single quantum dots (QDs) grown in inverted tetrahedral pyramids. The emitted light was detected for two mutually perpendicular linear polarization directions in the less conventional cleaved-edge geometry, in addition to the standard top-emission geometry. Whereas the in-plane linear polarization was isotropic, as a consequence of the high symmetry of the system, we found a strong polarization anisotropy of the edge-emitted light revealing QD states of predominantly heavy- or light-hole character. By temperature control of the charge state, several neutral and charged light-hole like exciton complexes were identified. In particular, a biexciton showing a twofold radiative recombination path, leading to two nearly perpendicularly polarized emission multiplets, was identified. These results are also of technological relevance for any design of optoelectronic QD-integrated devices.