Question

A polyhedron has 15 edges and 10 vertices. Find the number of faces.

Answer 1

By the Euler's relation for polyhedra, We know that
Number of faces + Number of vertices = Number of edges + 2
or $F+V=E+2$
Given: Number of edges = 15
Number of vertices = 10
Let the number of faces = x
Now putting these values in the Euler's relation, we get
$F+V=E+2$
$\Rightarrow x+10=15+2$
$\Rightarrow x=15+2-10$
$\Rightarrow x=7$
Therefore, number of faces = 7.