Kelvin polycrystals with geometrical packing of tetrakaidecahedra grains were regarded as the only possible stable polycrystalline structures in solids. By intensive plastic straining of Pt, we identified the existence of Kelvin polycrystals with 4 nm grains and Schwarz crystals of 2-3 nm in size connected by minimal-surface grain boundaries, both constrained by twins. We found Schwarz crystals remained stable up to 1923 K, nearly 94% of the melting point of Pt, well above the stability limit of the Kelvin polycrystals (1373 K). It means geometries of grains and their boundary networks play a crucial role in stabilizing polycrystalline face-centered-cubic metals at the nanoscale.