  A metallic covalently bonded carbon allotrope is predicted via first
principles calculations. It is composed of an $sp^3$ carbon framework that acts
as a diamond anvil cell by constraining the distance between parallel
cis-polyacetylene chains. The distance between these $sp^2$ carbon atoms
renders the phase metallic, and yields two well-nested nearly parallel bands
that span the Fermi level. Calculations show that this phase is a conventional
superconductor, with the motions of the $sp^2$ carbons being key contributors
to the electron phonon coupling. The $sp^3$ carbon atoms impart superior
mechanical properties, with a predicted Vickers hardness of 48~GPa. This phase,
metastable at ambient conditions, could be made via cold compression of
graphite to 40~GPa. A family of multifunctional materials with tunable
superconducting and mechanical properties could be derived from this phase by
varying the $sp^2$ versus $sp^3$ carbon content and by doping.
