Novel ultra-hard carbon allotropes are proposed based on crystal chemistry rationale and geometry optimization onto ground state structures. Like diamond, new orthorhombic, tetragonal, and trigonal C6 are identified as cohesive networks of C4 tetrahedra illustrated by charge density projections exhibiting sp3-like carbon hybridization. The three allotropes are mechanically (elastic constants) and dynamically (phonons) stable. Furthermore, they exhibit thermal properties like those of diamond. The electronic band structures are characteristic of insulators with large band gaps of 4 to 5 eV. From four different models evaluating Vickers hardness new carbon allotropes are identified as ultra-hard with HV close to 95 GPa.