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Which of the following can not be true for a polyhedron?

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V=4,F=4,E=6

V=6,F=8,E=12

V=20,F=12,E=30

V=4,F=6,F=6

answer is D.

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Detailed Solution

Euler's formula for any polyhedron :

F+V-E=2

Substitute all the given values,

Option (A),

4+4-6=2

=> 2=2

Option (B),

8+6-12=2

=>2=2

Option(C),

20+12-30=2

=>2=2

Option(D),

6+4-6=4

=>4 is not equal to 2.

Hence option (D) is incorrect

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