Question

The number of vertices in polyhedron which has 30 edges on 12 faces is
1. 12
2. 15
3. 20
4. 24

Answer 1

Correct Answer - Option 3 : 20

Given:

The edges of the polyhedron = 30

The faces of the polyhedron = 12

Formula used:

Euler's formula for the polyhedron

F + V = E + 2      (Where F = The face of the polyhedron, V = The vertices of the polyhedron, and E = The edge of the polyhedron)

Calculation:

Let be assume the vertices of the polyhedron is V

⇒ 12 + V = 30 + 2

⇒ V = 32 - 12 = 20

∴ The required result will be 20.