The injection mold has a mold core including a first part and a second part. The parts are mobile relative to one another between a first injection position in which they are moved together to form an injection cavity permitting the injection of a material to form an injected part (50; 50′), and a second demolding position in which they are moved away from one another to permit the demolding of the injected part (50; 50′). The injection mold has at least one ejector designed to contribute to the demolding, and at least one movable intermediate plate (10; 10′, 20′), separate from the two parts of the mold core. The intermediate pate is arranged between the two parts of the mold core, and has at least one cutout (12; 12′, 22′) forming at least one part of the injection cavity of the injection mold.