Here's an example of an order $96_6$ configuration found by L.W. Berman. Every point has six lines, every line has six points.

96_6 configuration

The unique 6,6 cage graph is bipartite and is a Levi graph for the following set of 31 lines.


Is there some way of arranging 31 points so that the corresponding pseudolines/splines/curves/lines/ellipses going the points is reasonably nice and symmetric?

EDIT: It occurs to me that these lines might be equivalent to the order-31 difference set generated by {1, 5, 11, 24, 25, 27}. That turns out to be true, here's the 6,6 cage with a difference-set based embedding.

cage 6,6

  • $\begingroup$ My Mathematica-fu isn't what it should be. Could you provide the adjacency matrix for the graph you want to embed? $\endgroup$ – Blue Apr 18 at 16:40
  • $\begingroup$ Blue: I'm looking for a configuration, not a graph. $\endgroup$ – Ed Pegg Apr 18 at 16:59

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