Planar Graph: external/unbounded face

Question

G is a planar graph.

E is an arbitrary edge of G.

"There exists a planar drawing of G where E is on the unbounded face of the drawing."

Why is the above statement true? Any help is appreciated.

Answer 1

One possible approach: Given a drawing, we can use inverse stereographic projection to get the drawing onto a sphere. Rotating and then projecting back allows us to make any face the unbounded one.