Recent photoluminescence spectra of positively charged excitons in InAs/GaAs quantum dots have revealed the existence of large splittings between the View the MathML sourcep-shell triplet sublevels of holes. We provide an intuitive explanation for their origin in terms of heavy hole-light hole coupling using Luttinger spinors. These splittings are present even in symmetric quantum dots at zero field and their magnitude can be tuned by the geometry of the dot. We show that the spin purity of the triplet drastically decreases with the aspect ratio, but that of the singlet ground state remains high.