Carbon is well-known as an insulator, a semimetal, a molecular solid,
and a one-dimensional semiconductor or low-density-of-states metal. We
propose a pure-carbon planar structure composed of pentagons and hept
agons that is metallic with a density of states at the Fermi level of
similar to 0.1 state per eV per atom. This structure, planar carbon pe
ntaheptite, is metastable with a total energy per carbon atom comparab
le to that of C-60. The structure can be rolled into tubes in a manner
similar to graphite. Possible synthetic pathways are discussed.