A pentagonal pyramid has 6 faces, 6 vertices and 10 edges. Find its Euler characteristic.

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Solution

The correct option is D 2
The Euler's formula for polyhedron is
$V - E + F = χ$
Where
$χ$ = Euler characteristic
$V$ = number of vertices = $6$
$E$ = number of edges = $10$
$F$ = number of faces = $6$
So,
$6 - 10 + 6 = χ$
$χ = 12 - 10$
$χ = 2$

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