SiGe Stranski-Krastanow islands coherently grown on Si(001) substrates by liquid phase epitaxy are typically made of truncated pyramids with {111} side facets, whereas the persistent presence of an (001) top facet indicates an energetical disadvantage of complete pyramids compared to truncated ones.We attribute this to a surface minimization process during the island evolution under the assumption of isotropically distributed surface energies and stable island facets. For the presence of {111} side facets we have theoretically derived a final geometrical aspect ratio of island base versus island height of 1.96, which is in excellent agreement with the experimentally derived averaged value of (2.08 +/- 0.10) within a concentration window between 9% and 30% germanium.