The structures and energetics of water clusters (H2O)20 and (H2O)21H+ have been studied by using gradient corrected density functional theory and empirical intermolecular potentials (SPC). For (H2O)20 both the empirical and ab initio methods favor rather compact structures with 4-fold coordinated molecules and not a fullerene-like pentagonal dodecahedron. In the case of (H2O)21H+ we find a structure with 4-fold coordinated molecules basically degenerate (∼1 kcal/mol lower in energy) with a filled pentagonal dodecahedron. However, the lower energy structure is significantly less compact than the neutral (H2O)20 structures, showing that the proton has a profound effect on the structure. Most of the (H2O)21H+ structures studied here have 10 non-hydrogen-bonded hydrogens and thus are compatible with the experiments of Castleman and co-workers.