V - E + F = 2

where

V = number of vertices
E = number of edges
F = number of faces





Tetrahedron

V = 4

E = 6

F = 4

4 - 6 + 4 = 2








Cube

V = 8

E = 12

F = 6

8 - 12 + 6 = 2








Octahedron

V = 6

E = 12

F = 8

6 - 12 + 8 = 2








Dodecahedron

V = 20

E = 30

F = 12

20 - 30 + 12 = 2








Icosahedron

V = 12

E = 30

F = 20

12 - 30 + 20 = 2








Buckyball

V = 60

E = 90

F = 32 (12 pentagons + 20 hexagons)

60 - 90 + 32 = 2







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Higher-dimensional versions of Euler's formula.