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Question
Can a polyhedron have V = F = 9 and E = 16? If yes, draw its figure.
Solution
Given, Vertices = 9, Face = 9 and Edges = 16
Using Euler's formula for polyhedron,
F + V – E = 2 ...[Where, F = faces, V = vertices and E = edges]
⇒ 9 + 9 – 16 = 2
⇒ 18 – 16 = 2
⇒ 2 = 2
Hence, the given values satisfies the Euler's formula.
So, a polyhedron can have V = F = 9 and E = 16.
Thus, we can draw a octagonal pyramid.
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