  We study dimensional trends in ground states for soft-matter systems.
Specifically, using a high-dimensional version of Parrinello-Rahman dynamics,
we investigate the behavior of the Gaussian core model in up to eight
dimensions. The results include unexpected geometric structures, with
surprising anisotropy as well as formal duality relations. These duality
relations suggest that the Gaussian core model possesses unexplored symmetries,
and they have implications for a broad range of soft-core potentials.
