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