A rigid core at least partially defining a manufacturing form for the internal surface of a tire, the core including a plurality of circumferentially adjacent fractions disposed side by side in contact with one another by their transverse faces, the transverse faces of at least one fraction converging radially at the exterior of the core, each of the fractions including a portion for attachment to a rim, the attachment portion being arranged at the radially internal end of each of the fractions, the attachment portion being produced essentially from a first material, the core further including a main portion which is integrally connected to the attachment portion, is produced essentially from a second material different from the first material and is integrally connected to the attachment portion, the manufacturing form being essentially defined by said main portion.