I am having trouble proving this:
"Let $P$ be a convex polyhedron with $V$ vertices, $E$ edges and $F$ faces. Furthermore, let $F_m$ be the number of faces surrounded by $m$ edges, and let $V_m$ be the number of vertices from which $m$ edges emanate.
Show that every convex polyhedron contains a face with either 3, 4 or 5 edges.
Show that every convex polyhedron contains a vertex from which either 3, 4 or 5 edges emanate."
There is apparently a proof by contradiction for these but I have no idea how or where to start with it.