For any convex polyhedron, a formula that establishes a relationship between the number of vertices

*, the number of faces***V***and the number of edges***F***, such that:***E***+***V***=***F***+ 2.***E**### Examples

- In this pentagonal prism, there are 10 vertices (
*V*), 7 faces (*F*) and 15 edges (*E*).

Therefore, the relationship is: 10 + 7 = 15 + 2. - In a connected graph (network), the relationship among the number of nodes
, the number of regions**N**and the number of edges (or arcs)**R**, such that:**E**+**N**=**R**+ 2.**E**

In the connected graph below, there are 6 nodes (), 4 regions (**N**) and 8 edges (**R**).**E**

Therefore, the relationship is: 6 + 4 = 8 + 2.