if no three diagonals of a convex polygon are concurrent at a point in the interior, the number of interior intersections of diagonals is given by formula_3. this holds, for example, for any regular polygon with an odd number of sides. the formula follows from the fact that each intersection is uniquely determined by the four endpoints of the two intersecting diagonals: the number of intersections is thus the number of combinations of the "n" vertices four at a time.