Euler's Formula
For any convex polyhedron, a formula that establishes a relationship between the number of vertices V, the number of faces F and the number of edges E, such that: V + F = E + 2.
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 N, the number of regions R and the number of edges (or arcs) E, such that: N + R = E + 2.
In the connected graph below, there are 6 nodes (N), 4 regions (R) and 8 edges (E).
Therefore, the relationship is: 6 + 4 = 8 + 2.
