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Question
Check whether a polyhedron can have V = 12, E = 6 and F = 8.
Solution
By using Euler's formula for polyhedron,
F + V – E = 2 ...[Where, F = faces, V = vertices, E = edges]
⇒ 8 + 12 – 6 = 2
⇒ 20 – 6 = 2
⇒ 14 ≠ 2
∴ Given values do not satisfy the Euler's formula. It mean this type of polyhedron cannot be possible.
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