Question

Using Euler’s formula, find the unknowns.

S. No.	Faces	Vertices	Edges
(i)	?	6	14
(ii)	8	?	10
(iii)	20	10	?

Answer 1

Euler’s formula is given by F + V- E = 2

(i) V = 6, E = 14

By Euler’s formula

= F + 6 – 14 = 2

F = 2 + 14 – 6

F = 10

(ii) F = 8, E = 10

By Euler’s formula

= 8 + V – 10 = 2

V = 2 – 8 + 10

V = 4

(iii) F = 20, V = 10

By Euler’s formula

= 20 + 10 – E = 2

30 – E = 2

E = 30 – 2

E = 28

Tabulating the required unknowns

S. No.	Faces	Vertices	Edges
(i)	10	6	14
(ii)	8	4	10
(iii)	20	10	28