Recently I am learning the basic knowledge of drawing theory of planar graph, and I refer to the following book.
Nishizeki, Takao, and Md Saidur Rahman. Planar graph drawing. Vol. 12. World Scientific, 2004.
A straight line drawing of a plane graph $G$ is called a convex drawing if the boundaries of all faces of $G$ are drawn as convex polygons, as illustrated in following picture.
There is an exercise on page 16 of the book about showing that the following three graphs have no convex drawing.
Obviously, the third graph with multiple edges cannot be drawn with straight lines drawing.
So there must have no convex drawing. But for the first two, I have not yet explained why they do not have convex drawing.
