Question

If a polyhedron has 8 faces and 12 edges, then how many vertices it has ?​

Answer 1

Answer:

No. of vertices = 6.

Step-by-step explanation:

According to the Euler's formula, there is a fixed relationship between the edges, vertices and the faces.

As we know,

V = E + 2 - F

V = 12 + 2 - 8

V = 14 - 8

V = 6

:) Thank you!

Answer 2

The polyhedron has 6 vertices

Given :

A polyhedron has 8 faces and 12 edges

To find :

The number of vertices of the polyhedron

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 = 8

E = Number of edges = 12

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

⇒ 8 + V = 12 + 2

⇒ V + 8 = 14

⇒ V = 14 - 8

⇒ V = 6

The polyhedron has 6 vertices

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