Math Is Fun Forum

The relation in the number of vertices, edges and faces of a polyhedron gives Euler's Formula. By using Euler's Formula, V+F=E+2 can find the required missing face or edge or vertices.Euler's law states that  'For any real number x, e^ix = cos x + i sin x. This complex exponential function is sometimes denoted cis x ("cosine plus i sine"). The formula is still valid if x is a complex number. Abstract: “V − E + F = 2”, the famous Euler's polyhedral formula, has a natural generalization to convex polytopes in every finite dimension, also known as the Euler– Poincaré Formula. We provide another short inductive combinatorial proof of the general formula.For solid shapes, especially polyhedra, the sum of the faces and vertices will be 2 more than their edges. Faces + vertices = edges + 2. Another way of writing this is Faces + vertices - edges = 2. This is known as Euler's formula.