  We report a systematic study of the spin relaxation anisotropy between single
electron Zeeman sublevels in cuboidal GaAs quantum dots (QDs). The QDs are
subject to an in-plane magnetic field. As the field orientation varies, the
relaxation rate oscillates periodically, showing ``magic'' angles where the
relaxation rate is suppressed by several orders of magnitude. This behavior is
found in QDs with different shapes, heights, crystallographic orientations and
external fields. The origin of these angles can be traced back to the
symmetries of the spin admixing terms of the Hamiltonian. In [001] grown QDs,
the suppression angles are different for Rashba and Dresselhaus spin-orbit
terms. By contrast, in [111] grown QDs they are the same, which should
facilitate a thorough suppression of spin-orbit induced relaxation. Our results
evidence that cubic Dresselhaus terms play a critical role in determining the
spin relaxation anisotropy even in quasi-2D QDs.
