How do you determine Euler's characteristics?
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Mathematicians often compute a number called the Euler Characteristic for a surface to identify it. For a surface we would create a pattern on the surface made up of vertices, edges and faces. The Euler Characteristic formula is X = V - E + F. Here we see 6 vertices, 12 edges and 8 faces.
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The Euler characteristic is equal to the number of vertices minus the number of edges plus the number of triangles in a triangulation. Normally it's denoted by the Greek letter χ, chi (pronounced kai); algebraically, χ=v-e+f, where f stands for number of faces, in our case, triangles.
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