Refill for inserting into a device for treating the hair by pivoting

A hair treating device, comprising:

• two arms that are able to move relative to one another between a moved-together configuration for treating the hair and a spaced-apart configuration for inserting hair to be treated between said arms, one of the arms comprising a housing,
• a cosmetic refill disposed in a removable manner in the housing comprising:
• a body that has a first wall and a second wall opposite the first wall and that defines between them a cavity, the cavity opening toward the outside at least by way of an opening of the body,
• an applicator member for applying a cosmetic product to the hair inserted in the cavity that extends at least partially through the opening of the body,
• (i) a coupling relief on the first wall being intended to cooperate with a first surface of the housing when the first wall is introduced into the housing, and
• (ii) an elastically deformable coupling tongue connected at a first end thereof to the second wall by way of a rounded portion, the coupling tongue having an inner surface spaced from and facing the second wall, an outer surface opposite the inner surface and a second end opposite the first end, wherein the coupling tongue is configured to cooperate with a second surface of the housing when the cosmetic refill is brought into a use position in the hair treating device by pivoting the cosmetic refill in the housing about a pivot axis, the opening of the cavity extends along a plane that is perpendicular to the pivot axis,
• at least one protruding relief on the outer surface between the first and second ends configured to be inserted into a recessed relief in the second surface of the housing, or at least one recessed relief on the outer surface between the first and second ends for receiving a protruding relief on the second surface of the housing,
• wherein the coupling tongue extends along a longitudinal axis perpendicular to a longitudinal axis of the refill and perpendicular to the pivot axis, the second wall having first and second ends defining a width therebetween, the width measured in a direction parallel to the coupling tongue, such that a first axis extending from the first end and intersecting the longitudinal axis of the coupling tongue defines a first abscissa at the intersection thereof, and a second axis extending from the second end and intersecting the longitudinal axis of the coupling tongue defines a second abscissa at the intersection thereof, and wherein the protruding relief or the recessed relief on the coupling tongue is positioned between the first and second abscissas, and a third abscissa positioned at the second end along the longitudinal axis of the coupling tongue, the distance between the third and the first abscissas being greater than the distance between the second and the first abscissas, a distance between the third and the second abscissas being greater than or equal to 1 mm, the coupling tongue extending substantially parallel to the second wall, wherein the space between the inner surface and the second wall is between 1 and 5 mm, wherein the coupling tongue has at least one griping relief disposed between the third and second abscissas.