Mechanical and electronic properties of hypothetical carbon nanostructures, on the basis of C₂₈ building blocks, hyperdiamond and hyperlonsdaleite, have been investigated with DFT based methods. The low mass density and large internal surface suggest applications as catalyst, nanosieve and gas storage material. We estimate the active volume accessible by H₂. Special emphasis is given to the possibility to tune their properties by endo- and exohedral intercalation with Zn, Ti and K. While endohedral intercalation with Zn does not affect the overall structure, endohedral Ti intercalation has different consequences on the structural stability of the two allotropes. Exohedral intercalation with K leads to an ionic fullerite phase with metallic conductivity.