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Symmetry and Recognition of Solids Test - 1

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    A polyhedron has 14 faces and 24 vertices. What is the number of edges of the polyhedron?

    Solution

    By Euler’s formula, we know that for a polyhedron,

    F + V − E = 2, where F, V, and E are the number of faces, vertices, and edges of the polyhedron.

    Now, F = 14 and V = 24

    ∴ 14 + 24 − E = 2

    ⇒ E = 38 − 2 = 36

    Thus, the required polyhedron has 36 edges.

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