A convex polyhedron has 20 vertices and 12 faces. Each face of the polyhedron is bounded by the same number of edges. What is this common number?
If I am not mistaken , "this common number" is the number of edges which cover one face.
So to find this i tried following: $n =$ # of verices $e =$ # of edges $r =$ # of regions or faces
$n = 20$, $r = 12$
We know that polyhydron must be connected plane graph (No intersections of edges and faces). If we apply Euler's Polyhedral Theorem: $n-e+r=2$ we get that $e=30$. We know that sum of degrees is $2 e$, so $\sum(d(v))=60$ . Therefore the degree of each vertex is 3. Now i am stuck! What should I do now?