The structural, electronic, and vibrational characteristics and energies of the isolated polyoxide clusters B20O30, Al20O30, V20O50, Si20O30H20, and Si20O30F20 and their complexes with the H− ion and ammonia complexes Al20O30 · nNH3 have been calculated by the density functional theory B3LYP method with different basis sets. The computation results show that the symmetric closo structure Ih with oxygen bridges located above the centers of the faces of an empty [M20] dodecahedron is more favorable for V20O50, Si20O30H20, and Si20O30F20. For B20O30, the cage closo isomer is also more favorable than the other isomers, but its structure is severely distorted as compared to a dodecahedron and has a symmetry close to C3. For Al20O30, the Ih structure corresponds to a high-lying local minimum of the potential energy surface. For Al20O30, a set of unusual puckshaped isomers of symmetry Ci, with different numbers of four-coordinate atoms IVAl and three-coordinate atoms IIIO, was localized; these structures are more than 90 kcal/mol more favorable than the dodecahedron Ih. The most favorable isomer of Al20O30 contains twelve four-coordinate atoms IVAl and four five-coordinate atoms VAl. The energies of dissociation of the most favorable M20O30 clusters into the M2O3 (C2v) and M4O6 (Td) fragments and, in the case of Al20O30, also into the Al8O12 (Oh) and Al12O18 (D3d) fragments, have been estimated. The conclusion has been drawn that these clusters can, in principle, exist and can be experimentally detected in the isolated state. Analogous calculations have been performed for ammonia complexes Al20O30 · nNH3 with n varying from 1 to 20. The effect of solvation on the relative stability of the dodecahedral and puckshaped isomers of the Al20O30 cluster is observed. The isomers with ammonia molecules in their first coordination sphere become much closer to one another on the energy scale; however, the dodecahedron remains a considerably less favorable intermediate.