The lines containing the three points of the intersection of the three pairs of opposite sides of a (not necessarily regular) hexagon. There are 6! (i.e., 6 factorial) possible ways of taking all polygon vertices in any order, but among these are six equivalent cyclic permutations and two possible orderings, so the total number of different hexagons (not all simple) is (6!)/(2·6) = 720/12 = 60. There are therefore a total of 60 Pascal lines created by connecting polygon vertices in any order.

Cayley lines | heptagon theorem | hexagon | Kirkman points | Pascal's theorem | Plücker lines | Salmon points | Steiner points

Blaise Pascal