An instrument for applying a composition to hair or nails includes a core made as a single piece that extends longitudinally along a mean longitudinal axis. The instrument includes a plurality of applicator projections for applying the composition to hair or nails. The applicator projections are carried by the core and are spread out helically along the core. The helical spreading of the projections is obtained by twisting the core. The projections are disposed on the core, prior to twisting the core, along at least three distinct radial directions about the mean longitudinal axis. The instrument further includes a twister element to which the core is attached such that the twisted nature of the core is imparted by the twister element.