Question

Can a polyhedra have $10$ faces, $20$ edges and $15$ vertices?

• A. Yes
• B. No
• C. Depends on dimension
• D. None of these

Answer 1

The correct option is B No

Given: No. of face(F):10

No. of edges(E):20

No. of vertices(V):15

According to Euler formula, we know that

F + V = E + 2

That is, here

10 + 15 = 20 + 2

⇒ 25 = 22

This is not true.(That is, 25≠22 )

∴ A polyhedra with 10 faces, 20 edges and 15 vertices is not possible.