Example of two star shaped polygons on the plane such that every edge of the first polygon is intersected by every edge of the second one internally

Question

This question was asked in my computational geometry exam yesterday. The definition of a star shaped polygon was given as: A polygon is called star-shaped if there is a point inside it such that the whole boundary is visible from that point.

Since every edge of the first polygon must intersect every edge of the second, I first arranged the edges in a grid. I then connected them in a shark teeth fashion. But I couldn't manage to close the ends while still maintaining the intersection criteria. Any ideas on how this could be done?

Answer 1

Don't mind if I answer my own question :)

The trick is to literally "close the ends". And pick fewer lines, it'll be simpler to depict.

As you can see, the polygons are star shaped and the edges mutually fully intersect.