Which of the following cannot be true for a polyhedron?

# Which of the following cannot be true for a polyhedron?

1. A
V = 4, F = 6 and E = 6
2. B
V = 20, F = 12 and E = 30
3. C
V = 16, F = 18 and E = 32
4. D
V = 4, F = 4 and E = 6

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### Solution:

We know Euler’s formula for Polyhedron is
F + V = E + 2
Where F is the number of faces, V denotes the number of vertices, and E denotes the number of edges.
Let us check for each given option.
Check for option (1) V = 4, F = 6 and E = 6.
F + V - E
= 6 + 4 - 6
= 4 ≠ 2
So, this option is correct.
The correct option is (1).

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