Generalized Polygon

Author

Eric W. Weisstein
January 30, 2008

This notebook downloaded from http://mathworld.wolfram.com/notebooks/GraphTheory/GeneralizedPolygon.nb.

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

©2008 Wolfram Research, Inc. except for portions noted otherwise

Figure

GP[n_,l_]:="G"<>Switch[n,4,"Q",6,"H",8,"O",12,"D"]<>"("<>StringTake[ToString[l],{2,-2}]<>")"

gp=GraphData["GeneralizedPolygon"]

GraphData["Tutte12Cage","StandardNames"]

(l=Sort[{GraphData[#,"V"],GraphData[#,"Name"],GP@@("GeneralizedPolygon"/.GraphData[#,"NotationRules"])}&/@gp])//TableForm//TraditionalForm

GraphicsGrid[Partition[GraphPlot[Graph[#],PlotLabel->TextCell[GP@@("GeneralizedPolygon"/.GraphData[#,"NotationRules"])<>"\n"<>GraphData[#,"Name"],TextAlignment->Center,PageWidth->120],BaseStyle->{FontSlant->"Italic"},Method->None]&/@SortBy[Select[gp,GraphData[#,"Embeddings"]=!={}&],GraphData[#,"V"]&],4,4,{1,1},{}],ImageSize->500,Spacings->{-50,40}]

Cubic

GraphData[{"GeneralizedPolygon","Cubic"}]