Fill in the blank.

A polyhedron has 60 edges and 40 vertices then the number of its faces is ____.

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Detailed Solution

A polyhedron has 60 edges and 40 vertices then the number of its faces is 22.
It is given that,

V = 40 and E = 60

.
We know that, Euler’s formula for any polyhedron is

F + V - E = 2

where F is the face of the polyhedron, V is the vertices of the polyhedron and E is the edges of the polyhedron.
On putting given values in Euler’s formula,

F + 40 - 60 = 2

\Rightarrow F - 20 = 2

\Rightarrow F = 20 + 2

\Rightarrow F = 22

Therefore, the number of faces is 22.
Hence, a polyhedron has 60 edges and 40 vertices then the number of its faces is 22.

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