A polyhedron is a solid bounded by F plane faces, which meet in E edges and V vertices. You may assume Euler’s formula, that $V − E + F = 2$.
In a regular polyhedron the faces are equal regular m-sided polygons, n of which meet at each vertex. Show that
$F =\frac{4n}{h}$ , where $h = 4 − (n − 2)(m − 2)$
By considering the possible values of h, or otherwise, prove that there are only five regular polyhedra, and find V , E and F for each.
I'm stuck on the second part of this question. I've tried bounding h by saying that the number of faces meeting at a point can be a maximum of $\frac{2\pi}{\theta}$ where $\theta$ is the interior angle. But I realise now that obviously doesn't show anything.
I was wondering if I could get a good hint as to a first step as I'm not sure how it wants me to look at the possible values of h.
Thanks in advance :)