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]

⇒ 9 + 9 – 16 = 2

⇒ 18 – 16 = 2

⇒ 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.