Question

Verify Euler’s formula for each of the following polyhedrons:

Answer 1

(i) Vertices = 10

Faces = 7

Edges = 15

By using Euler’s formula

V + F = E + 2

10 + 7 = 15 + 2

17 = 17

Hence verified.

(ii) Vertices = 9

Faces = 9

Edges = 16

By using Euler’s formula

V + F = E + 2

9 + 9 = 16 + 2

18 = 18

Hence verified.

(iii) Vertices = 14

Faces = 8

Edges = 20

By using Euler’s formula

V + F = E + 2

14 + 8 = 20 + 2

22 = 22

Hence verified.

(iv) Vertices = 6

Faces = 8

Edges = 12

By using Euler’s formula

V + F = E + 2

6 + 8 = 12 + 2

14 = 14

Hence verified.

(v) Vertices = 9

Faces = 9

Edges = 16

By using Euler’s formula

V + F = E + 2

9 + 9 = 16 + 2

18 = 18

Hence verified.