Reduced ceria (CeO_2-x) has a rich phase diagram comprising a variety of bulk phases with stoichiometries ranging from CeO₂ to Ce₂O₃ as the reduction conditions are increased. Some observed reduced ceria (111) surface reconstructions are terminations of stable bulk phases, such as √7×√7, whereas others are not associated with any known stable phases, namely, √7×3, 3×3, and √3×√3. In this paper, we analyze different periodic reconstructions of reduced ceria (111) surfaces within a theoretical framework. We describe the surfaces of stable bulk phases and elucidate the structure of the observed periodicities not corresponding to terminations of known stable bulk phases. Extending the 3×3 and √3×√3 terminations into a bulk structure, we find a new quasistable Ce₃O₅ bulk phase, which explains both periodicities. On the contrary, the √7×3 surface structure cannot be extended into a bulk but stabilizes as a very thin overlayer. We also analyze other reported bulk structures with stoichiometry close to the Ce3O5 one, namely, the C-type Ce₂O_3+δ bulk phase, which cannot describe the observed terminations. Our goal is to provide a unified picture to describe the road map of CeO_2-δ(111) surface reconstructions and, when possible, their relationship to reduced ceria bulk phases.