The invention provides an injection mold core (100) for making a composite material part having a closed box, the core being in the shape of a wedge that is to be inserted inside a closed box (12) of at least one fiber preform into which a matrix-precursor fluid is to be injected, the core presenting both an opening right section (106) through which the core is to be unmolded from the box of the preform after the matrix has set, and also a maximum right section (108) of greater size than the opening right section, the core comprising at least three distinct elements (110, 112, 114) that are assembled together, each core element presenting a maximum right section of size that is smaller than the opening section.