How can I use OpenGL to define a polygon by it’s edge rather than it’s vertices?

Thank you.

??? what?
How do you want to specify it’s position in 3D space if you don’t have the start and end of a line? You either need the begging of the line, the end of it, and you can do it with the centre of it as well, by calculating the beggining and end. But why do you want to do that? It’s not practicall.

Or, to answer with a question: How do you define an edge without its vertices/endpoints?