On the Clebsch diagonal cubic, all 27 of the complex lines present on a general smooth cubic surface are real. In addition, there are 10 points on the surface where three of the 27 lines meet. These points are called Eckardt points (Fischer 1986).
Eckardt Point
See also
Clebsch Diagonal Cubic, Cubic SurfaceExplore with Wolfram|Alpha
References
Fischer, G. (Ed.). Mathematische Modelle aus den Sammlungen von Universitäten und Museen, Kommentarband. Braunschweig, Germany: Vieweg, p. 11, 1986.Referenced on Wolfram|Alpha
Eckardt PointCite this as:
Weisstein, Eric W. "Eckardt Point." From MathWorld--A Wolfram Web Resource. https://mathworld.wolfram.com/EckardtPoint.html