To fully meet the diversified needs of market, auto end-locked cartons of n prisms (frustum) symmetrical structure folding carton were extended. The design of non-molding working score of auto end-locked structure is critical. Here, our study focused on the third glued point to a variety of multi prisms (frustum) symmetric structure cartons; the first, second, third non molding working score of auto end-locked carton were defined, and the third non-molding working score of auto end-locked carton with n prisms (frustum) was proposed (n≥5). When the auto end-locked carton was designed with n(either odd or even) prisms(frustum) and symmetric structure, the third non molding working score was the axisymmetric line of the main bottom panel, which was the bisector of one or two diagonal angles of the bottom. The starting point was determined by molding working score of carton body or the bottom projection location of the first non molding working score, which was the key to the design of auto end-locked carton with n prisms(frustum) and symmetrical structure. Taken together, the third non molding working score of auto end-locked carton was proposed, which can increase adhesive area, improve bottom strength, and make the type of auto end-locked cartons more diversified.