Up: The Euler Number

The Euler Numbers for the Platonic Solids

The tetrahedron

    Four triangular faces

    V = 4
    E = 6
    F = 4

    V - E + F = 4 - 6 + 4 = 2

The cube

    Six square faces

    V = 8
    E = 12
    F = 6

    V - E + F = 8 - 12 + 6 = 2

The octahedron

    Eight triangular faces

    V = 6
    E = 12
    F = 8

    V - E + F = 6 - 12 + 8 = 2

The icosahedron

    Twenty triangular faces

    V = 12
    E = 30
    F = 20

    V - E + F = 12 - 30 + 20 = 2

The dodecahedron

    Twelve pentagonal faces

    V = 20
    E = 30
    F = 12

    V - E + F = 20 - 30 + 12 = 2



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