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Which of the following cannot be true for a polyhedron?

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Which of the following cannot be true for a polyhedron?

(a) V = 4, F = 4, E = 6 

(b) V = 6, F = 8, E = 12

(c) V = 20, F = 12, E = 30 

(d) V = 4, F = 6, E = 6

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Best answer

(d) V = 4, F = 6, E = 6

We have,

Euler’s formula for any polyhedron is, F + V – E = 2

Where, face (F) = 6, Vertex (V) = 4, Edge (E) =6

Then,

6 + 4 – 6 = 2

LHS 6 + 4 -6

10 – 6

4

RHS = 2

By comparing LHS and RHS

LHS ≠ RHS

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