We demonstrate by spin quantum beat spectroscopy that in undoped symmetric (110)-oriented GaAs/AlGaAs single quantum wells even a symmetric spatial envelope wavefunction gives rise to an asymmetric in-plane electron Land\'e-g-factor. The anisotropy is neither a direct consequence of the asymmetric in-plane Dresselhaus splitting nor of the asymmetric Zeeman splitting of the hole bands but is a pure higher order effect that exists as well for diamond type lattices. The measurements for various well widths are very well described within 14 x 14 band k.p theory and illustrate that the electron spin is an excellent meter variable to map out the internal -otherwise hidden- symmetries in two dimensional systems. Fourth order perturbation theory yields an analytical expression for the strength of the g-factor anisotropy, providing a qualitative understanding of the observed effects
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