# Eulers formula

**Euler's formula** A formula that states necessary but not sufficient conditions for an object to be a *simple polyhedron*. An object with *V* vertices, *E* edges, and *F* faces satisfies the formula χ = *V* – *E* + *F*

where χ is called the *Euler characteristic* of the surface in which the object is embedded. For a plane connected graph, the formula takes the form *V* – *E* + *F* = 1

For a simple polyhedron in Euclidean 3-space, the formula has the form *V* – *E* + *F* = 2

A simple polyhedron is any polyhedron that can be continuously deformed into a sphere, assuming that its faces are treated like sheets of rubber. All faces are bounded by a single ring of edges: there are no holes in the faces; each edge joins exactly two faces and is terminated by a vertex at each end. At least three edges meet at each vertex.

#### More From encyclopedia.com

#### You Might Also Like

#### NEARBY TERMS

**Eulers formula**