Density functional theory (DFT) at the hybrid B3LYP level has been applied to the germanium clusters Ge-11(z) (z = -6, -4, -2, 0, +2, +4, +6) starting from eight different initial configurations. The global minimum within the Ge-11(2-) set is an elongated pentacapped trigonal prism distorted from D-3h to Q(2v) symmetry. However, the much more spherical edge-coalesced icosahedron, also of C-2v symmetry, expected by the Wade-Mingos rules for a 2n + 2 skeletal electron system and found experimentally in B11H112- and isoelectronic carboranes, is of only slightly higher energy (+5.2 kcal/mol). Even more elongated D-3h pentacapped trigonal prisms are the global minima for the electron-rich structures Ge-11(4-) and Ge-11(6-). For Ge-11(4-) the C-5v 5-capped pentagonal antiprism analogous to the clicarbollide ligand C2B9H112- is of significantly higher energy (∼ 28 kcal/mol) than the D-3h global minimum. The C-2v edge-coalesced icosahedron is also the global minimum for the electron-poor Gel, similar to its occurrence in experimentally known 11-vertex "isocloso" metallaboranes of the type (η(6)-arene)RuB10H10. The lowest energy polyhedral structures computed for the more hypoelectronic Ge-11(4+) and Ge-11(6+) clusters are very similar to those found experimentally for the isoelectronic ions E-11(7-) (E = Ga, In, Tl) and Tl9Au29- in intermetallics in the case of Ge-11(4+) and Ge-11(6+), respectively. These DFT studies predict an interesting D-5h centered pentagonal prismatic structure for Ge-11(2+) and isoelectronic metal clusters.