Question

Question 73

A polyhedron has 60 edges and 40 vertices. Find the number of its faces.

Answer 1

By using Euler's formula for polyhedron.
F + V - E = 2 [where, F = faces, V = vertices, E = edges]
$\Rightarrow$ F + 40 - 60 = 2 [$\therefore$ E = 60 and V = 40, given]
$\Rightarrow$ F- 20 = 2
$\Rightarrow$ F = 2 + 20
$\Rightarrow$ F = 22
Hence, the number of faces are 22