Crossing bridges and colouring maps - an introduction to topology, part 2

The second in a two-part introduction to topology in which, among other things, we meet the bridges of Konigsberg and the four colour theorem.

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A very enjoyable presentation. I know that a sphere is topologically equivalent to each of the platonic solids, so it makes sense that the Euler Characteristic V - E + F should equal 2 for the sphere, as it does for the other shapes. But the sphere has no vertices or edges and has just one face. So shouldn't V - E + F = 1 for the sphere?