Euler characteristic

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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 amount of points in the shape, the amount of lines in the shape, and the amount of faces of the shape. Then, you find the Euler characteristic with this formula:

\chi=V-E+F \,\!

V is the point count, E the line count, and F the amount of faces. For most common shapes, the Euler Characteristic is 2.

Name Image Vertices (Points)
V
Edges (Lines)
E
Faces
F
Euler characteristic:
VE + F
Tetrahedron Tetrahedron.png 4 6 4 2
Hexahedron or cube Hexahedron.png 8 12 6 2
Octahedron Octahedron.png 6 12 8 2
Dodecahedron Dodecahedron.png 20 30 12 2
Icosahedron Icosahedron.png 12 30 20 2