When I looked up the definition of convex drawing of planar graph, my confusion mainly focused on the outer face.

The following definition of convex drawing is from Wikipedia.

In graph drawing, a

convex drawingof a planar graph is a drawing that represents the vertices of the graph as points in the Euclidean plane and the edges as straight line segments, in such a way that all of the faces of the drawing (including the outer face) have a convex boundary.

It gives two examples

Surprisingly, the outer face is not convex in the second example.

I 'd like to ask what is the convex boundary of outer face here? The outer face doesn't seem to be convex and I feel that **the unbounded face is the complement of a convex set.**

So **I'm confused by the definition of convex drawing where boundary of the outer face is also convex**. I don't know where I got it wrong.

I searched the Mathemaics Stack for a similar puzzle below. There seems to be no consensus. https://math.stackexchange.com/questions/940693/convex-planar-graphs