body 2 has a profiled shape with radius of curvature r 13 joined to swelling d 3 and the front face 18 of the front body 4 has a profiled shape with radius of curvature r 11 joined to the swelling d 1 these radii of curvature r 13 and r 11 are equal as can also be seen in said figures the rear body 2 has towards the front a thinned down profiled shape formed by a hollow b 14 of radius of curvature r 14 joined to the rear of the front body 4 the front body 4 has towards the rear a thinned down profiled shape formed by a hollow b 12 of radius of curvature r 12 joined to the front of the rear body 2 these radii of curvature r 14 and r 12 are equal as clearly shown in fig3 the projectile may be intended to be crimped to a case e as shown the case e is crimped to the rear body 2 in the hollow b 14 situated in front of swelling d 3 a shallow groove g may then be provided at this location in said rear body the front part 14 of the central core 1 cooperates with the front body 4 through an axial abutment surface 33 as shown in the embodiment illustrated in fig4 a 4b the rear body 2 comprises a rear swelling b.