Given, say, a hexagon, we can construct a new one by the following procedure. This procedure gives 6 new points. The figure shows two of these points. The solid cyan point is where the line determined by 6 and 2 intersects the line determined by 1 and 3. In the ordering of the points, 6 comes before 1, and plays the role of 0 in the construction.

Of course, there's nothing special about hexagons. We could make the same construction, in the same way, for any polygon. On an octagon, we would call this construction the octagram. On a 10-gon, we would call this construction the 10-gram And so on.