Question

Using Euler’s formula, find the unknown.​

Faces	?	5	20
Vertices	6	?	12
Edges	12	9	?

Answer 1

Find the number of faces
Given
$V=6\text{and}E=12$
Using Euler's formula : $F+V-E=2$
$F+6-12=2$
$F=2+12-6$
$F=14-6$
$F=8$

Find the number of vertices
Given $F=5\text{and}E=9$
As $F+V-E=2$
$V=1+9-5$
$V=11-5$
$V=6$

Find the number of edges
Given $F=20\text{and}V=12$
$20+12-E=2$
$32-E=2$
$E=32-2$
$E=30$

Hence the unknowns are :

Faces	8	5	20
Vertices	6	6	12
Edges	12	9	30