The structures and energetics of centered 10-vertex Ge@Ge10 z (z = −4, −2, 0, +2, +4) clusters have been investigated by density functional theory (DFT) for comparison with the previously studied isomeric empty 11-vertex Ge11 z clusters. For the cationic species (z = +2, +4) such centered Ge@Ge10 z structures are shown to be energetically competitive (within ∼1 kcal mol−1) to the lowest energy isomeric empty Ge11 z structures. These Ge@Ge10 z structures can be derived from the lowest energy empty 10-vertex Ge10 z−4 structures by inserting a Ge4+ ion in the center. The outer 10-vertex polyhedron in the lowest energy Ge@Ge10 2+ dication structure is the most spherical D 4d bicapped square antiprism, which is also the lowest energy structure of the empty Ge10 2− dianion, as expected from the Wade-Mingos skeletal electron counting rules. For the tetracationic Ge11 4+/Ge@Ge10 4+ system the lowest energy centered Ge@Ge10 4+ structure can be obtained by inserting a Ge4+ ion in the center of a C 3v deltahedral empty Ge10 cluster. Centered 10-vertex polyhedral Ge@Ge10 z structures were also found for the neutral (z = 0) and dianionic (z = −2) systems but at significantly higher energies than the lowest energy isomeric empty Ge11 z structures.