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Schläfli Double Six


SchlaefliDoubleSix

The Schläfli double six is a (12_530_2) configuration consisting of two sextuples of skew lines on the general cubic surface such that each line of one is skew to one line in the other set. In all, there are 30 points, with two lines through each point, and 12 lines with five points on each line. Two lines can be placed in the plane of each of the faces of a cube. The double six was discovered by Schläfli.

The Levi graph of the double six is the Schläfli double six graph.


See also

Configuration, Cubic Surface, Skew Lines, Solomon's Seal Lines

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References

Fischer, G. (Ed.). Mathematische Modelle aus den Sammlungen von Universitäten und Museen, Kommentarband. Braunschweig, Germany: Vieweg, p. 11, 1986.Wells, D. The Penguin Dictionary of Curious and Interesting Geometry. London: Penguin, p. 224, 1991.

Cite this as:

Weisstein, Eric W. "Schläfli Double Six." From MathWorld--A Wolfram Web Resource. https://mathworld.wolfram.com/SchlaefliDoubleSix.html

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