  We provide rigorous evidence that the ordered ground state configurations of
a system of parallel oriented, ellipsoidal particles, interacting via a
Gaussian interaction (termed in literature as Gaussian core nematics) {\it
must} be infinitely degenerate: we have demonstrated that these configurations
originate from the related ground state configuration of the corresponding
symmetric Gaussian core system via a suitable stretching operation of this
lattice in combination with an arbitrary rotation. These findings explain
related observations in former investigations, which then remained unexplained.
Our conclusions have far reaching consequences for the search of ground state
configurations of other nematic particles.
