Test Your Intuition (58): Polyhedra with 5-sided and 6-sided faces.

Let F be the class of planar 3-connected cubic graphs with n vertices, with all faces (including the outer face) are either pentagons or hexagons. Equivalently, F can be viewed as the family of graphs of simple 3-polytopes with n vertices and only 5-sided and 6-sided faces.

Test your intuition: Does the number of graphs in F with n vertices grows exponentially or polynomially with n?