To start, think of a regular n-gon inscribed in a circle. If the vertices of the n-gon are all connected by drawing cords between the other vertices, then another smaller n-gon is created at the center of the circle, the "zero cell."
The zero cell contains the center of the circle, and thus by definition, it is unique.
What happens if instead of being evenly spaced, the n points are "randomly" selected from the circumference of the circle? On average, how many sides are to be expected? What would be the distribution of the number of sides of the zero cell?
Edited for clarity about how zero cell is constructed.
Edited again to specify that zero cell contains the center of the circle.