Structural models of growing Ge hut clusters-pyramids and wedges-are proposed on the basis of data of recent STM investigations of nucleation and growth of Ge huts on the Si(001) surface in the process of molecular beam epitaxy. It is shown that extension of a hut base along <110> directions goes non-uniformly during the cluster growth regardless of its shape. Growing pyramids, starting from the second monolayer, pass through cyclic formation of slightly asymmetrical and symmetrical clusters, with symmetrical ones appearing after addition every fourth monolayer. We suppose that pyramids of symmetrical configurations composed by 2, 6, 10, etc. monolayers over the wetting layer are more stable than asymmetrical ones. This might explain less stability of pyramids in comparison with wedges in dense arrays forming at low temperatures of Ge deposition. Possible nucleation processes of pyramids and wedges on wetting layer patches from identical embryos composed by 8 dimers through formation of 1 monolayer high 16-dimer nuclei different only in their symmetry is discussed. Schematics of these processes are presented. It is concluded from precise STM measurements that top layers of WL patches are relaxed when huts nucleate on them.