Line segment where two surfaces of a geometric solid meet.

In a solid, an edge is a segment at the intersection of two plane or curved surfaces.

### Property

Euler’s formula can be applied in polyhedra that can be represented using a connected graph. In this case, the sum of the number of vertices (V) and faces (F) is equal to the number of edges (E) plus 2, that is: S + F = A + 2.

### Examples

V + F = A + 2 8 + 6 = 12 + 2 |
V + F = A + 2 9 + 9 = 16 + 2 |

The polyhedron shown below cannot be represented by a connected graph. Therefore, Euler’s formula cannot be applied.

V + F ≠ A + 2 16 + 11 ≠ 24 + 2 27 ≠ 26 |
This graph is disconnected. |