Negative-curvature fullerene analog of ${\mathrm{C}}_{60}$

An analog of the ${\mathrm{C}}_{60}$ buckyball structure is investigated, in which seven-fold rings play the same role as the five-fold rings of ${\mathrm{C}}_{60}$. This periodic ${\mathrm{C}}_{168}$ structure is topologically ideal in the same sense as ${\mathrm{C}}_{60}$: Every atom is in a topologically equivalent local environment, participating in one seven-fold and two six-fold rings. The excess energy per atom to create this structure from an ideal graphitic sheet is predicted to be substantially less than for ${\mathrm{C}}_{60}$. If this material could be synthesized, we predict that it would have elastic constants comparable to those of Si, but with a density nearly half that of graphite.