The 60 Pascal lines of a hexagon inscribed in a conic intersect three at a time through 20 Steiner points, and also three at a time in 60 Kirkman points. Each Steiner point lies together with three Kirkman points on a total of 20 lines known as Cayley lines. The 20 Cayley lines pass four at a time though 15 points known as Salmon points. There is a dual relationship between the 20 Cayley lines and the 20 steiner points.

Kirkman points | Pascal lines | Pascal's theorem | Plücker lines | Salmon points | Steiner points