Question

Question 49

State whether the following statement is True or False.

A polyhedron can have 10 faces, 20 edges and 15 vertices.

Answer 1

False
We know that, Euler's formula satisfies for every polyhedron.
i.e. F + V - E = 2
Here, F = 10, E = 20 and V = 15
On putting these values in the Euler's formula, we get
10 + 15 - 20 = 2
$\Rightarrow$ 25 - 20 = 2
$\Rightarrow$ 5 $\ne$ 2
Hence, the given values does not satisfy the Euler's formula.