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

On the degeneracy of ordered ground state configurations of the aspherical Gaussian core model