which leads to the formation of a corresponding rib shaped projection in the barrel the advantages of the polygonal barrel are not impaired and thus through the preferred inventive measure of remaining outside of the caliber circle the gas seal and thus the muzzle velocity of the projectile as well as the higher life expectancy in comparison to barrels with the grooves and lands are not reduced and the easier cleaning of the interior of the barrel is also maintained the invention shall be explained in greater detail below through the use of the drawing figures in an exemplary embodiment of fig1 the cross section of polygonal barrel 1 with six linear polygonal segments 2 is depicted the inscribed circle 3 of which preferably the caliber circle corresponds to the caliber measurement the areas that lie outside of the caliber circle or the arched segments 4 offset the entire surface of the barrel cross section without the consideration of the ribs 5 on the entire cross section of the projectile in each of the six arched segments 4 is centrally located a rib 5 that extends radially inward their depth t of which is so small that neither the lateral walls of the rib 5 nor its end wall cuts the inscribed circle 3 and with this implementation the rib 5 lies completely outside the caliber circle or on the caliber circle fig3 and 4 depict an alternative exemplary embodiment with a triangular form of the ribs 5 and with an arrangement of the ribs 5 in the transition between the polygonal segments 2 and the arched segments 4 and consequently twelve ribs 5 are provided here as well their depth t is chosen in such a way as with the first.