According to Euler Characteristic Index Theorem V-E+F=0, we can conclude that there are
exactly 5 Platonic solids.The index of sphere(S

^{2}) is 2, and the index of torus is 0.

In this note, we introduce the difinition of simplex( convex combinition of vertices), we find Pascal
triangle in n-simplex, it is interesting.

The volume of n dimensional ball is interesting, for fixed radius, when n is 5, the volume is
maximum, when n approaches to infinity, the volume approaches to zero.