The kissing number of the regular pentagon

AbstractLet pn be an arbitrary regular polygon with n sides. What is the maximum number k(pn) of congruent regular polygons(copies of pn) that can be arranged so that each touches pn but no two of them overlap? Youngs (Amer. Meth. Monthly 46 (1939) 20), Klamkin et al. (Math Mag. 68 (1995) 128) and others established that k(p3)=12, k(p4)=8, and k(p6)=6. Likuan Zhao (Discrete Math. 188 (1998) 293) established that k(pn)=6(n>6). In this paper, we will establish k(p5)=6. Thus we prove the guess in Likuan Zhao and completely solve the kissing numbers of all regular polygons