Question

A polyhedron has 12 faces and 30 edges. Find the number of vertices.

• A. 50
• B. 10
• C. 20
• D. 30

Answer 1

The correct option is C 20

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 faces = 12
Number of edges = 30
Let,
The number of vertices = x
Now substituting these values in the Euler's relation, we get
$F+V=E+2$
$\Rightarrow 12+x=30+2$
$\Rightarrow x=30+2-12$
$\Rightarrow x=20$
Therefore, number of vertices = 20.