Rotor for an electric machine having internal permanent magnets, comprising a yoke formed by a stack of sheets defining a plurality of recesses (1 to 8) for receiving parallelepipedal permanent magnets (51 to 58), said recesses (1 to 8) forming pairs and being surrounded by magnetically saturated outer transverse isthmuses (11, 12) and lateral isthmuses (15, 16), and by radial isthmuses (10, 20, 30, 40) and oblique isthmuses (13, 14), characterized in that each: - radial isthmus (10, 20, 30, 40) extends radially from the center of the yoke of the rotor and passes between a pair of recesses (1 to 8); - outer transverse isthmus (11, 12) is perpendicular to the radial isthmus (10, 20, 30, 40) and positioned on the outer side of the recess (1 to 8); - oblique isthmus (13, 14) is located on the inner side of the recess (1 to 8) between the recess (1 to 8) and the center of the yoke of the rotor; - lateral isthmus (15, 16) is positioned between adjacent recesses (1 to 8) of each pair of recesses (1 to 8) and connects materials areas and the center of the yoke of the rotor; - said parallelepipedal permanent magnets (51 to 58) are assembled in pairs, each pair of parallelepipedal permanent magnets (51, 52) being magnetized in the same direction and perpendicularly to the radial direction of the radial isthmuses (10, 20, 30, 40) arranged between said paired parallelepipedal permanent magnets (51 to 58), - said radial isthmuses (10, 20, 30, 40) having a thickness of less than 5% of the diameter of the rotor, - and in that the periphery of the cross-section of the rotor is formed by a succession of curvilinear profiles and linear profiles, each curvilinear profile being formed between two consecutive pairs of parallelepipedal permanent magnets (51, 52), each linear profile, having a tangent direction, delimiting two outer transverse isthmuses (11, 12) of a pair of consecutive recesses (1 to 8). - radial isthmus (10, 20, 30, 40) extends radially from the center of the yoke of the rotor and passes between a pair of recesses (1 to 8); - outer transverse isthmus (11, 12) is perpendicular to the radial isthmus (10, 20, 30, 40) and positioned on the outer side of the recess (1 to 8); - oblique isthmus (13, 14) is located on the inner side of the recess (1 to 8) between the recess (1 to 8) and the center of the yoke of the rotor; - lateral isthmus (15, 16) is positioned between adjacent recesses (1 to 8) of each pair of recesses (1 to 8) and connects materials areas and the center of the yoke of the rotor; - said parallelepipedal permanent magnets (51 to 58) are assembled in pairs, each pair of parallelepipedal permanent magnets (51, 52) being magnetized in the same direction and perpendicularly to the radial direction of the radial isthmuses (10, 20, 30, 40) arranged between said paired parallelepipedal permanent magnets (51 to 58), - said radial isthmuses (10, 20, 30, 40) having a thickness of less than 5% of the diameter of the rotor, - and in that the periphery of the cross-section of the rotor is formed by a succession of curvilinear profiles and linear profiles, each curvilinear profile being formed between two consecutive pairs of parallelepipedal permanent magnets (51, 52), each linear profile, having a tangent direction, delimiting two outer transverse isthmuses (11, 12) of a pair of consecutive recesses (1 to 8).