A hair cutting kit (10) comprises a cutting unit (30) and a comb (60). The comb (60) comprises a row of comb teeth (70). Some or all of the comb teeth (70) comprise, on an outer face, a skin surface (71) configured to glide on a user's skin, a feeding surface (72) configured to feed hairs towards the cutting unit, and a transition surface (73) between the skin surface and the feeding surface. The skin surface has a first surface contour line (81) having a first radius of curvature (R S ), the feeding surface has a second surface contour line (82) having a second radius of curvature (R F ), and the first radius of curvature is greater than the second radius of curvature.