Question

Can a polyhedron have V = F = 9 and E = 16 ? If yes, draw its figure.

Answer 1

Given, vertices = 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.