I'm new here and I'm having difficulty with this graph theory question.
Suppose $G$ is a connected $3$-regular planar graph which has a planar embedding such that every face has degree either $5$ or $6$. I need to prove that $G$ has precisely $12$ faces of degree $5$.
I know that a $3$-regular graph is a graph where all the vertices are of degree $3$ and that a planar embedding is a graph that has no edges crossing.