Möbius-Kantor Configuration

Author

Eric W. Weisstein
December 1, 2007

This notebook downloaded from http://mathworld.wolfram.com/notebooks/Combinatorics/Moebius-KantorConfiguration.nb.

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

©2007 Wolfram Research, Inc. except for portions noted otherwise

Source

Figure

Mean[{{-1/2,0},{0,Sqrt[3]/2}}]

RegionIntersection[Line[{{-1/2,0},{1/4,(Sqrt[3])/4}}],Line[{{0,0},{-1/4,(Sqrt[3])/4}}]]//FullSimplify

points={{-1/2,0},{0,0},{1/2,0},{0,Sqrt[3]/2},{-(1/4),((Sqrt[3])/4)},{(1/4),((Sqrt[3])/4)},{(1/8),((Sqrt[3])/8)},{-(1/8),((Sqrt[3])/8)}};

lines={{1,2,3},{3,6,4},{4,5,1},{2,7,6},{2,8,5},{3,7,5},{1,8,6}};
circles={{4,7,8}};

Graphics[{Line[points[[#]]]&/@lines,Circumsphere[points[[#]]]&/@circles,{Red,PointSize[.02],Point[points]},MapIndexed[Text[#2[[1]],#,1.5{-1,-1},Background->White]&,points]}]

incidences=Join[lines,circles]

LeviGraph[incidences]//RecognizeGraph