Applicator for applying a cosmetic product to human keratin materials, having: a holder and an applicator tip (20), of longitudinal axis (X), that is carried by the holder and has: a base part (22), of axis (X), for fastening to the holder by way of at least one of its portions, and an application part (24) that is attached to the base part (22) and has at least three surfaces (26, 28, 30), each having a contour formed by at least one edge (34), and/or a base line (36) that acts as a junction between the application part (24) and a cylindrical portion, of axis (X), of the base part (22), the shapes of the contours of the surfaces (26, 28, 30) being different in pairs and not symmetrical to one another about an axis or a median plane.