Question

How is Euler's Formula defined for solid figures?

Answer 1

Solution :-

Euler's formula for any polyhedron that doesn't intersect itself,

the Number of Faces + Number of Vertices - the Number of Edges = 2

This can be written : F + V - E = 2

Some examples are as follows.

Name Faces Vertices Edges F + V - E

Tetrahedron 4 4 6 2

Cube 6 8 12 2

Octahedron 8 6 12 2

Dodecahedron 12 20 30 2

Icosahedron 20 12 30 2