  We study the influence of quantum dot symmetry on the Rabi frequency and
phonon induced spin relaxation rate in a single electron GaAs spin qubit. We
find that anisotropic dependence on the magnetic field direction is independent
of the choice of the gating potential. Also, we discover that relative
orientation of the quantum dot, with respect to the crystallographic frame, is
relevant in systems with ${\bf C}_{1{\rm v}}$, ${\bf C}_{2{\rm v}}$, or ${\bf
C}_{n}$ ($n\neq4r$) symmetry. To demonstrate the important impact of the gating
potential shape on the spin qubit lifetime, we compare the effects of an
equilateral triangle, square, and rectangular confinement with the known
results for the harmonic potential. In the studied cases, enhanced spin qubit
lifetime is revealed, reaching almost six orders of magnitude increase for the
equilateral triangle gating.
