  From crystal chemistry rationale and density functional DFT calculations,
novel tetragonal carbon C5 is proposed as simplest ultrahard allotrope with
mixed hybrid carbon hybridizations (sp2 - sp3). Novel pentacarbon is identified
as cohesive and stable both dynamically and mechanically. Whereas charge
density is localized about tetrahedral C-sp3, it is found delocalized around
trigonal C-sp2 resulting in metallic behavior. The anisotropic structure
characteristics caused by the aligned trigonal carbon along the tetragonal
c-axis provide high Vickers hardness with a magnitude close to diamond
