Fano Plane

Author

Eric W. Weisstein
December 15, 2022

This notebook downloaded from http://mathworld.wolfram.com/notebooks/Combinatorics/FanoPlane.nb.

For more information, see Eric's MathWorld entry http://mathworld.wolfram.com/FanoPlane.html.

©2022 Wolfram Research, Inc. except for portions noted otherwise

Figure

p1={{-1,0},{1,0},{0,Sqrt[3]}};
points=Join[p1,Mean/@Partition[p1,2,1,1],{Mean[p1]}];
lines={{1,7,5},{2,7,6},{3,7,4},{1,6,3},{3,5,2},{1,4,2}};
circ={4,5,6};

Graphics[{PointSize[.02],Point[points],MapIndexed[Text[#2[[1]],#,2{-2,-1}]&,points],Circumsphere[points[[circ]]],Line[points[[#]]]&/@lines}]

Levi graph

RecognizeGraph@LeviGraph[Append[lines,circ]]