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Euler's Formula

Rule

Euler's Formula

The sum of the number of faces and vertices of a polyhedron is two more than the number of its edges .

As an example, this can be verified for the following polyhedron.

The above polyhedron has faces, vertices, and edges.

Rule

Euler's Formula in Two Dimensions

Euler's formula takes a slightly different form in two dimensions.

Here, is the number of regions formed by vertices, linked by segments. This formula can be verified for the net of the previous polyhedron.

The net shown has regions, vertices, and segments.