Anyone who knows anything about Mathematics knows Euler’s Formula connecting the number of faces (F), edges (E) and vertices (V) of polyhedra.
F – E + V = 2
(A cube for example has 6 faces, 12 edges and 8 vertices so that 6 – 12 + 8 = 2).
But what if the shape has a hole in it? (Click the picture to go to the file)
Does the formula change? If so how does it change? And the most important question, why does it change?
Further to this, what if the the shape has 2 holes, 3 holes, …, n holes? How does this affect the formula?