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We performed B3PW and B3LYP computations for BaTiO₃ (BTO), CaTiO₃ (CTO), PbTiO₃ (PTO), SrTiO₃ (STO), BaZrO₃ (BZO), CaZrO₃ (CZO), PbZrO₃ (PZO) and SrZrO₃ (SZO) perovskite neutral (001) along with polar (011) as well as (111) surfaces. For the neutral AO- as well as BO₂-terminated (001) surfaces, in most cases, all upper-layer atoms relax inwards, although the second-layer atoms shift outwards. On the (001) BO₂-terminated surface, the second-layer metal atoms, as a rule, exhibit larger atomic relaxations than the second-layer O atoms. For most ABO₃ perovskites, the (001) surface rumpling <i>s</i> is bigger for the AO- than BO₂-terminated surfaces. In contrast, the surface energies, for both (001) terminations, are practically identical. Conversely, different (011) surface terminations exhibit quite different surface energies for the O-terminated, A-terminated and BO-terminated surfaces. Our computed ABO₃ perovskite (111) surface energies are always significantly larger than the neutral (001) as well as polar (011) surface energies. Our computed ABO₃ perovskite bulk B-O chemical bond covalency increases near their neutral (001) and especially polar (011) surfaces.