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Let B be a solid such that each face is either a square, a pentagon or...

Let B be a solid such that each face is either a square, a pentagon or a hexagon. Furthermore, the solid B has no holes in it. Using Euler’s formula, prove that the number of squares, S, and the number of pentagons, P, in B satisfy the formula 2S + P = 12, assuming that exactly 3 faces meet at each vertex.

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