Metals usually exist in the form of polycrystalline solids, which are thermodynamically unstable because of the presence of disordered grain boundaries. Grain boundaries tend to be eliminated through coarsening when heated or by transforming into metastable amorphous states when the grains are small enough. Through experiments and molecular dynamics simulations, we discovered a different type of metastable state for extremely fine-grained polycrystalline pure copper. After we reduced grain sizes to a few nanometers with straining, the grain boundaries in the polycrystals evolved into three-dimensional minimal-interface structures constrained by twin boundary networks. This polycrystalline structure that underlies what we call a Schwarz crystal is stable against grain coarsening, even when close to the equilibrium melting point. The polycrystalline samples also exhibit a strength in the vicinity of the theoretical value.