Using Euler’s formula find the unknown


Faces



?



5



20



Vertices



6



?



12



Edges



12



9



?



By Euler's formula, we have

F + V - E = 2


(i) F + 6 - 12 = 2


F - 6 = 2


F = 8


(ii) 5 + V - 9 = 2


V - 4 = 2


V = 6


(iii) 20 + 12 - E = 2


32 - E = 2


E = 30


Thus, the table can be completed as:


Faces



8



5



20



Vertices



6



6



12



Edges



12



9



30



7
1