Euler's Polyhedron Formula

Leonhard Euler discovered a very simple formula that links every polyhedron.

A polyhedron is a three dimensional solid that has flat faces and straight edges. The points at which edges meet are called vertices.

‘Vertices’ is the plural of vertex. A vertex is another name for a corner of a shape.

Leonhard Euler discovered a formula that connects the number of Vertices (V), Edges (E) and Faces (F) in any polyhedron.

Face (F)

Vertex (V)

Edge (E)

V - E + F = 2

Test the formula for a cube, and then try it on different solid shapes with different numbers of vertices, edges and faces.

For which of the solids below does the formula fail?

Why does the formula fail for this solid?