Physical properties, such as stability, electronic properties, hole effective mass, electron effective mass, mechanical properties, structural properties, and optical properties of P6 3 /mmc-Ge 6 and their Si 6-x Ge x (x=1, 2, 3, 4, 5) alloys are investigated using ab initio calculations based on density functional theory. The anisotropic mechanical properties of the Young's modulus of Si 6-x Ge x alloys are all slightly superior than those of diamond-Si, while the Young's modulus of Si 6-x Ge x alloys in the (001) plane are isotropic (E max =E min ). With the increase in the number of germanium atoms, Si 5 Ge and Si 4 Ge 2 exhibit direct band gaps of 0.63 eV and 0.18 eV, respectively. All other Si 6-x Ge x (x=3, 4, 5) alloys and P6 3 /mmc-Ge 6 exhibit metallicity properties. In addition, the effective masses of electrons and heavy holes of Si 4 Ge 2 along the x and y directions become substantially smaller than those of Si 6 and Si 5 Ge.