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Self-assembled In 0.60 Ga 0.40 As quantum dots (QD's) have been studied by single dot magnetophotoluminescence spectroscopy (B≤ 8 T). At B= 0 a splitting of the exciton (X) emission is observed which we ascribe to an asymmetry of the confinement potential. With increasing B the emission splits into a quadruplet corresponding to the m=±2 and±1 X states, which originates from a reduction of the cubic symmetry of the QD's. From the spectroscopic data we obtain values for the electron (e) and hole (h) g factors. We also determine the X singlet-triplet splitting which is found to be enhanced over bulk values by about an order of magnitude due to the increase of the e− h overlap in the QD's.