question_answer 1)

                Using Euler's formula find the unknown.

	(i)	(ii)	(iii)
Faces	?	5	20
Vertices	6	?	12
Edges	12	9	?

 

Answer:

                (i) \[F+V=E+2\] \[\Rightarrow \]               \[F+6=12+2\] \[\Rightarrow \]               \[F+6=14\] \[\Rightarrow \]               \[F=146=8\] (ii) \[F+V=E+2\] \[\Rightarrow \]               \[5+V=9+2\] \[\Rightarrow \]               \[5+V=11\] \[\Rightarrow \]               \[V=115=6\] (iii) \[F+V=E+2\] \[\Rightarrow \]               \[20+12=E+2\] \[\Rightarrow \]               \[32=E+2\] \[\Rightarrow \]               \[E=32-2\] \[\Rightarrow \]               \[E=30\]