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Question
If the sum of number of vertices and faces in a polyhedron is 14, then the number of edges in that shape is ______.
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Solution
If the sum of number of vertices and faces in a polyhedron is 14, then the number of edges in that shape is 12.
Explanation:
Given, the sum of number of vertices and faces in a polyhedron is 14, i.e. V + F = 14
We know that, Euler’s formula, F + V – E = 2 for any polyhedron.
⇒ 14 – E = 2
⇒ 14 – 2 = E
⇒ E = 12
Hence, the number of edges are 12.
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