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 (Wells 1991). There is a dual relationship between the 20 Cayley lines and the 20 steiner points.
Cayley Lines
See also
Kirkman Points, Pascal Lines, Pascal's Theorem, Plücker Lines, Salmon Points, Steiner PointsExplore with Wolfram|Alpha
References
Johnson, R. A. Modern Geometry: An Elementary Treatise on the Geometry of the Triangle and the Circle. Boston, MA: Houghton Mifflin, pp. 236-237, 1929.Salmon, G. "Notes: Pascal's Theorem, Art. 267" in A Treatise on Conic Sections, 6th ed. New York: Chelsea, pp. 379-382, 1960.Wells, D. The Penguin Dictionary of Curious and Interesting Geometry. London: Penguin, p. 172, 1991.Referenced on Wolfram|Alpha
Cayley LinesCite this as:
Weisstein, Eric W. "Cayley Lines." From MathWorld--A Wolfram Web Resource. https://mathworld.wolfram.com/CayleyLines.html