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A new, globally regular model describing a static, non spherical gravitating object in General Relativity is presented. The model is composed by a vacuum Weyl-Levi-Civita special field - the so called gamma metric - generated by a regular static distribution of mass-energy. Standard requirements of physical reasonableness such as, energy, matching and regularity conditions are satisfied. The model is used as a toy in investigating various issues related to the directional behavior of naked singularities in static spacetimes and the black hole (Schwarzschild) limit.