Question
Can a polyhedron have $V = F = 9$ and $E = 16$? If yes, draw its figure.
✓
Answer
Given, vetices $= 9$, faces $= 9$ and edges $= 16$Using Euler's formula for polyhedron,$ F + V - E = 2$
[where, $F =$ faces, $V =$ vertices and $E =$ edges]
$\Rightarrow 9 + 9 -16 = 2$
$\Rightarrow 18 - 16 = 2$
$\Rightarrow 2 = 2$
Hence, the given values satisfies the Euler's formula. So, a polyhedron can have $V = F = 9$ and $E = 16$
Thus, we can draw a octagonal pyramid.
[where, $F =$ faces, $V =$ vertices and $E =$ edges]
$\Rightarrow 9 + 9 -16 = 2$
$\Rightarrow 18 - 16 = 2$
$\Rightarrow 2 = 2$
Hence, the given values satisfies the Euler's formula. So, a polyhedron can have $V = F = 9$ and $E = 16$
Thus, we can draw a octagonal pyramid.
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