Euler characteristic

In mathematics, the Euler characteristic of a shape is a number that describes a topological space, so that anything in the space will have the same number. It is calculated by taking the number of points in the shape, the number of lines in the shape, and the number of faces of the shape. One can find the Euler characteristic with this formula:

where V is the point count, E the line count, and F the face count. For most common shapes (convex polyhedron), the Euler characteristic is 2.

NameImageVertices (Points)VEdges (Lines)EFaces FEuler characteristic:V − E + FTetrahedron50px4642Hexahedron or cube50px81262Octahedron50px61282Dodecahedron50px2030122Icosahedron50px1230202
For spheres, the Euler characteristic is also 2.

 Related pages 

 Platonic solid

 References 

Category:Topology
Category:Graph theory