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Four sp3 carbon allotropes with six, eight, and 16 atoms per primitive cellhave been derived using a combination of metadynamics simulations andtopological scan. A chiral orthorhombic phase oC16 (C2221) was found to beharder than monoclinic M-carbon and shows excellent stability in thehigh-pressure range. A second orthorhombic phase of Cmmm symmetry, by \sim0.028 eV/atom energetically lower than W-carbon, can be formed from graphite at\sim 9 GPa. In general, the mechanical response under pressure was found todepend on the structure topology, which reflects the way rings are formed froman initial graphene layer stacking.

Superhard sp3 carbon allotropes with odd and even ring topologies