Check whether a polyhedron can have V = 12, E = 6 and F = 8.

Solution:

Given, V = 12

F = 8

E = 6

We have to determine if the given values satisfy Euler’s formula.

Euler’s formula for any polyhedron is given by

F + V - E = 2

Where F stands for number of faces,

V for number of vertices

E for number of edges.

Now, F + V - E = 8 + 12 - 6

= 20 - 6

= 14

The given values do not satisfy Euler’s formula.

Therefore, a polyhedron cannot have V = 12, E = 6 and F = 8.

✦ Try This: Check whether a polyhedron can have V = 14, E = 12 and F = 20.

☛ Also Check: NCERT Solutions for Class 8 Maths Chapter 10

NCERT Exemplar Class 8 Maths Chapter 6 Problem 72

Check whether a polyhedron can have V = 12, E = 6 and F = 8.

Summary:

A polyhedron cannot have V = 12, E = 6 and F = 8.

☛ Related Questions:

• A polyhedron has 60 edges and 40 vertices. Find the number of its faces
• Find the number of faces in the given shapes
• A polyhedron has 20 faces and 12 vertices. Find the edges of the polyhedron