A suitable operation of removing a face, together with an edge so that V-E+F remains unchanged is called a collapse. The idea of the proof of Euler is to show that any network can be reduced to a point by a sequence of collapses. A network need not be always planar, it is possible to draw network on a curved surface. Let us look at a 2-sphere. A 2-sphere is topologically equivalent to a tetrahedron. A tetrahedron has 4 vertices, 6 edges and 4 faces. So V-E+F turns out to be 2. On the other hand, if we take two copies of the tetrahedron, remove the interior of the base from each copy and paste them together along the boundaries of their bases, then the figure that we get is again equivalent to a 2-sphere and for this figure V-E+F again turns out to be 2. This suggests that the expression V-E+F contains certain information about the sphere.