The present invention relates to a cosmetic assembly for making up and/or caring for keratin materials, comprising at least:—one container containing at least one solid cosmetic composition, the said composition comprising at least one liquid fatty phase, at least one wax and at least 5% by weight of pigments relative to the total weight of the said composition, and having a melting point of greater than 30° C., and—one application device for applying the composition, equipped with an application member comprising an application surface that is capable, in response to its movement in engagement with the keratin materials, of rotating about at least one axis or one centre of rotation.