Polyhedron by Euler's formula.

I'm going to introduce you into a field full of beautiful mathematical formulas and probably one of the most useful due to its broad applications in chemistry, engineering, maths... As I said we are going to enter within one of the most beautiful mathematical formulas, Euler's formula. Space dedicated to issues of geometric objects that are more or less daily, the polyhedra, including the cube, triangular pyramid or tetrahedron, dodecahedron (whose faces are pentagons), the truncated icosahedron (the soccer ball), etc ... 

The study of polyhedra is of vital importance not only for the geometric study of them, for mathematical research, but also for its applications in diverse fields such as chemistry, mineralogy, biology, engineering, architecture, design or even art....

If  "C" represents all the faces of a simple polyhedron and "A" the polyhedron's number of edges/ridges and "V" represent the number of corners, then :

C+V-A = 2

The most outstanding fact is that doesn't matter how many cuts can displays a polyhedron, cause this cut is going to form another polyhedron and the relationship between them is going to be the same between its faces, corners, ridges/edges...( C+V-A=2).

Let's make an example of it.

We can see that this cube displays 6 faces (C=6), and also it displays 8 edges (V=8), and finally, we can see that the number of edges/ridges is equal to 12 (A=12).

So;

     C+V-A=2 -----------> 6+8-12 =14-12 = 2

And now, we can see here another a cut polyhedron, so as I mention the relationship has to be same as shown in the picture.