Question

A polyhedron have 24 edges and 10 faces . find the number of vertices .

Answer 1

F+V-E =2
10+V-24 =2
14-V =2
V =14+2
V =16

Answer 2

The number of vertices = 16

Given :

A polyhedron have 24 edges and 10 faces

To find :

The number of vertices

Concept :

Euler’s formula for Polyhedron :

For polyhedron F + V = E + 2

Where F stands for number of faces , V stands for number of vertices , E stands for number of edges

Solution :

Step 1 of 2 :

Write down number of faces , number of vertices , number of edges

F = Number of faces = 10

E = Number of edges = 24

V = Number of vertices = ?

Step 2 of 2 :

Find number of vertices

We use Euler’s formula

By Euler’s formula

F + V = E + 2

⇒ 10 + V = 24 + 2

⇒ V + 10 = 26

⇒ V = 26 - 10

⇒ V = 16

The number of vertices = 16

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