let be name the points as,(https://ibb.co/2srLjB1) if AC would be an edge then A and C are vertices and segments BC, AC, AD, CE became edges. Is this justified Also for a simple polygon there should be no self intersecting edge, the line AC just touches the lines BD and BE, is this sufficient to fulfill the intersecting condition?Yes, it could be described as a polygon - but not a "simple polygon".
If the left edge from top to bottom is A, B, D and the right edge from top to bottom is A, C, E:
Then this could be described as polygon ABCBDECA or ABCEDCDA.
Thus, it would be a polygon that intersects itself.
polygons that do not intersect themselves are called "simple polygons".
Oh, and to answer your follow-on question: The middle line segment would be two edges.
thanks for correcting.With your new point labels, the polygon would be either BACADECB or BADECACB.
In order for it to be a polygon, you need to close the loop - end at the same place you started.
I am not sure I am interpreting your statements correctly, but it doesn't sound as though you are following that rule.