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Hexagonal SiGe is a promising material for combining electronic and photonic technologies. In this work, the energetic, structural, elastic and electronic properties of the hexagonal polytypes (2H, 4H and 6H) of silicon and germanium are thoroughly analyzed under equilibrium conditions. For this purpose, we apply state-of-the-art density functional theory. The phase diagram, obtained in the framework of a generalized Ising model, shows that the diamond structure is the most stable under ambient conditions, but hexagonal modifications are close to the phase boundary, especially for Si. Our band-structure calculations using the MBJLDA and HSE06 exchange correlation functionals predict significant changes in electronic states with hexagonality. While Si crystals are always semiconductors with indirect band gaps, the hexagonal Ge polytypes have direct band gaps. The branch point energies for Ge crystals are below the valence band maxima, and therefore the formation of hole gases on Ge surfaces is favoured. Band alignment based on the branch point energy leads to type-I heterocrystalline interfaces between Ge polytypes, where electrons and holes can be trapped in the layer with the higher hexagonality. In contrast, the energy shift of the indirect conduction band minima of Si polytypes is rather weak, leading to delocalization of excited electrons at interfaces, while only holes can localize in the layer with higher hexagonality.