Are the edges of a planar graph part of its faces? (Graph Theory)

Question

The definition of face I have learned for planar graphs is "a region where any 2 points in it not on $G$ can be connected by a line which doesn't intersect any of the edges of $G$". I am wondering if this region would include the actual edges themselves- as it is vacuously true that points which lie on the edges can be connected by a line which doesn't intersect the edges (as I would translate the definition as being for any 2 points on the plane in $f$, if they are not in G and can be connected without intersecting an edge, then $f$ is a face of $G$, and for 2 points on $G$, the antecedent of the implication in my translation is false so the statement is vacuously true for these points).