A polyhedron has $12$ faces and $20$ vertices. How many edges does it have?

28

No worries! We‘ve got your back. Try BYJU‘S free classes today!

30

Right on! Give the BNAT exam to get a 100% scholarship for BYJUS courses

34

No worries! We‘ve got your back. Try BYJU‘S free classes today!

36

No worries! We‘ve got your back. Try BYJU‘S free classes today!

Open in App

Solution

The correct option is B $30$
A polyhedron is a platonic solid,
So, Euler's formula $F + V - E = 2$ applies.
Given,
$F = 12$ and $V = 20$
So, $12 + 20 - E = 2$
$\Rightarrow 32 - E = 2$
$\Rightarrow E = 32 - 2 = 30$
Therefore, a polyhedron has $30$ edges.

Suggest Corrections

Similar questions

A solid has $40$ faces $60$ edges how many vertices does it have.

Can a polyhedron have 20 faces, 12 vertices and 30 edges?

Join BYJU'S Learning Program