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Discrete Mathematics Level pending

A certain convex polyhedron has faces which are equilateral triangles and regular pentagons, and four faces meet at each vertex. Each triangle is surrounded by pentagons, and each pentagon is surrounded by triangles.

Let \( f_{n} \) be the number of \( n \) sided faces in the polyhedron, and let \( e \) and \( v \) be the number of edges and vertices respectively.

Find \( \dfrac{f_{3} \times e}{f_{5} \times v} \). Let it be of the form \( \dfrac{a}{b} \), where \( a \) and \( b \) are coprime natural numbers. Enter \( (a+b) \) as your answer.

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