  In recent years, nanostructures with hexagonal polytypes of gold have been
synthesised, opening new possibilities in nanoscience and technology. As bulk
gold crystallizes in the \textit{fcc} phase, surface effects can play an
important role in stabilizing hexagonal gold nanostructures. Here we
investigate several hetero-structures with Ge substrate, including the
\textit{fcc} and \textit{hcp} phases of gold that have been observed
experimentally. We determine and discuss their interfacial energies and
optimized atomic arrangements, comparing the theory results with available
experimental data. Our calculations for the Au-\textit{fcc}(011)/Ge(001) show
how the presence of defects in the interface layer can help to stabilize the
atomic pattern consistent with microscopic images. The Au-\textit{hcp}/Ge
interface with the significant mismatch between two surfaces reveals large
atomic displacements, which might indicate that the (111) germanium substrate
is not responsible for the formation of the \textit{hcp} phase of gold.
Finally, analyzing the electronic properties, we demonstrate that Au/Ge systems
have metallic character but covalent-like bonding states between interfacial Ge
and Au atoms are also present.
