Eulers formula

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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 = VE + 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 VE + F = 1

For a simple polyhedron in Euclidean 3-space, the formula has the form VE + 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.