The Number of Intersection Points Made by the Diagonals of a Regular Polygon
Bjorn Poonen and Michael Rubinstein
We give a formula for the number of interior intersection points made by the diagonals of a regular $n$-gon. The answer is a polynomial on each residue class modulo 2520. We also compute the number of regions formed by the diagonals, by using Euler's formula $V-E+F=2$.