Probing atomic clusters with magic numbers is of supreme importance but challenging in cluster science. Pronounced stability of a metal cluster often arises from coincident geometric and electronic shell closures. However, transition metal clusters do not simply abide by this constraint. Here, we report the finding of a magic-number cluster Rh ₁₉ ⁻ with prominent inertness in the sufficient gas-collision reactions. Photoelectron spectroscopy experiments and global-minimum structure search have determined the geometry of Rh ₁₉ ⁻ to be a regular O _h ‑[Rh@Rh ₁₂ @Rh ₆ ] ⁻ with unusual high-spin electronic configuration. The distinct stability of such a strongly magnetic cluster Rh ₁₉ ⁻ consisting of a nonmagnetic element is fully unveiled on the basis of its unique bonding nature and superatomic states. The 1-nanometer–sized O _h -Rh ₁₉ ⁻ cluster corresponds to a fragment of the face-centered cubic lattice of bulk rhodium but with altered magnetism and electronic property. This cluster features exceptional electron-spin state isomers confirmed in photoelectron spectra and suggests potential applications in atomically precise manufacturing involving spintronics and quantum computing.