According to Euler Characteristic Index Theorem V-E+F=0, we can conclude that there are
exactly 5 Platonic solids.The index of sphere(S2
) is 2, and the index of torus is 0.
Delaunay triangulation is the dual graph of Vonoroi graph, it is important in computational
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.