Question

The figure has 60 edges and 30 vertices. Use Euler’s formula to find the number of faces in the given polyhedron.

Answer 1

Let the number of faces ⇒⇒⇒ F
Number of Vertices ⇒⇒⇒ V
Number of Edges ⇒⇒⇒ E

Euler's Formula ⇒⇒⇒⇒⇒ F + V − E = 2

given:⇒⇒⇒ 60 edges and 30 vertices
∴ E = 60 and V = 30
∴ F + 30 - 60 = 2
∴ F = 2 + 60 - 30 = 32

Number of faces = 32