An analog of the C60 buckyball structure is investigated, in which seven-fold rings play the same role as the five-fold rings of C60. This periodic C168 structure is topologically ideal in the same sense as C60: 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 C60. 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. © 1992 The American Physical Society.