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Let G be a polyhedron (or polyhedral graph), each of whose faces is bounded by a pentagon or a hexagon. (i) Use Euler's formula to show that G must have at least 12 pentagonal faces. (ii) Prove, in addition, that if G is such a polyhedron with exactly three faces meeting at each vertex (such as a football), then G has exactly 12 pentagonal faces. | Numerade
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