An applicator for a cosmetic product, in particular mascara, comprises a twisted core and fibers which extend from the core and are held by the core, the core having a main longitudinal direction of extension, known as the main axis (X), and the core being rectilinear along the main axis (X). The fibers form an envelope (E) with their free ends, the envelope (E) comprising faces (F1-F4) which alternate about the main axis (X), the faces (F1-F4) being curved, a cross section made transversely to the main axis (X), known as the cross section, having a substantially polygonal shape so as to form edges between the curved faces (F1-F4).