a) besides the soccer ball shape (20 hexagons, 12 pentagons), are there other polyhedrons composed of just pentagons and hexagons? Using Euler's formula of polyhedrons, prove what other polyhedrons are made of pentagons and hexagons.

b) Is this breakdown of edges 50/50? That is, must there be an equal number of edges adjacent one pentagon and one hexagon as there are edges between two hexagons? If claim so, justify your claim and if you believe there is another ratio, explain why this ratio must be correct.