Question

Using Euler's formula find the unknown:

$\begin{array}{cccc}Faces& ?& 5& 20\\ Vertices& 6& ?& 12\\ Edges& 12& 9& ?\end{array}$

Answer 1

We know that Euler's formula is

Faces + Vertices =Edges +2

$\left(i\right)F+6=12+2\Rightarrow F+6=14$

$\Rightarrow F=14-6=8\therefore$ Faces =8

(ii)F+V=E+2

$\Rightarrow 5+V=9+2\Rightarrow 5+V=11$

$\Rightarrow V=11-5=6\therefore$ Vertices =6

(iii)F+V=E+2

$20+12=E+2\Rightarrow 32=E+2$

$\Rightarrow E=32-2=30\Rightarrow$ Edges =30