An assembly of 13 atoms can form highly symmetric architectures like those belonging to D3h, Oh, D5h, and Ih point groups. Here, using photoelectron imaging spectroscopy in combination with density functional theory (DFT) calculations, we present a simple yet convincing experimental signature for the selective formation of icosahedral cages of anionic silver clusters encapsulating a dopant atom of group 5 elements: M@Ag12- (M = V, Nb, and Ta). Their photoelectron images obtained at 4 eV closely resemble one another: only a single ring is observed, which is assignable to photodetachment signals from a 5-fold degenerate superatomic 1D electronic shell in the 1S21P61D10 configuration of valence electrons. The perfect degeneracy represents an unambiguous fingerprint of an icosahedral symmetry, which would otherwise be lifted in all of the other structural isomers. DFT calculations confirm that Ih forms are the most stable and that D5h, Oh, and D3h structures are not found even in metastable states.