The purpose of this paper is to predict the existence of novel 3D covalent ultra-hard carbon allotropes in view of synthesizing them eventually. Stability and spectroscopic characteristics of the rarely occurring tricarbon linear molecule from quantum chemistry calculations are extended to the solid state based on crystal chemistry considerations and quantum density functional theory ground state calculations letting devise rhombohedral rh-C3 (h-C9) and hexagonal h-C6 proposed as ultra-hard carbon allotropes like lonsdaleite. Two crystallographic different carbons forming linear C2-C1-C2 unit are characterized as sp3-like C2 with an angle of 106.17° smaller than ideal 109.4°, and sp1 C1. The calculated elastic constants are positive and their combinations obey the required stability criteria; furthermore they point to a strong anisotropy of the mechanical properties of the two allotropes rh-C3 (h-C9) and h-C6 with exceptionally large C33 values (1636 GPa and 1610 GPa, respectively), exceeding that of lonsdaleite (1380 GPa). The phonon dispersion curves stress furthermore the dynamical stability of the two carbon allotropes by showing positive frequencies throughout the hexagonal Brillouin zone. A significant separation between the highest frequencies of the optic modes illustrates the rigidity of the bonding within linear C3 building block and the whole structure. Both allotropes are characterized by large bulk moduli and high hardness values that are only slightly less than those of lonsdaleite and diamond. Weak metallic behavior of both new carbon allotropes were identified from electronic band structure calculations and explained by the mixed sp1-sp3 hybridizations, likewise other carbon allotropes from literature: m-C12 (sp1-sp2) and h-C18 (sp2-sp3).