The second, also called the Euler polyhedra formula, is a topological invariance (see topology) relating the number of faces, vertices, and edges of any polyhedron. It is written F + V = E + 2, where F is the number of faces, V the number of vertices, and E the number of edges.

Eulers formula deals with shapes called Polyhedra. A Polyhedron is a closed solid shape which has flat faces and straight edges. Eulers Formula does however only work for Polyhedra that follow certain rules. The rule is that the shape must not have any holes, and that it must not intersect itself.

2:146:03e^ix: Deriving Eulers Formula (TANTON Mathematics) - YouTubeYouTube

It is written F + V = E + 2, where F is the number of faces, V the number of vertices, and E the number of edges. A cube, for example, has 6 faces, 8 vertices, and 12 edges and satisfies this formula.

The first formula, used in trigonometry and also called the Euler identity, says eix = cos x + isin x, where e is the base of the natural logarithm and i is the square root of −1 (see irrational number). ...