Symmetry group of plane graphs
3-valent graphs
We call q_n the class of 3-valent, n-vertex plane graphs whose faces are q-gons or 6-gons. If q=5, then we obtain the fullerenes.
4-valent graphs
We call i-hedrite the class of 4-valent plane graphs whose faces are 2-, 3- or 4-gons and such that p2=8-i, p3=2i-8.