Polygram

Author

Eric W. Weisstein
December 16, 2004

This notebook downloaded from http://mathworld.wolfram.com/notebooks/Polygons/Polygram.nb.

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

©2005 Wolfram Research, Inc. except for portions noted otherwise

Enumeration

Connected

Flatten[Table[{n,#}&/@Select[Range[2,n/2],GCD[#,n]==1&],{n,4,8}],1]

Not Necessarily Connected

Flatten[Table[{n,#}&/@Range[2,(n-1)/2],{n,3,9}],1]

Figure

V5

MakeBoxes[label[{m_,n_}],TraditionalForm]:=RowBox[{"{",RowBox[{MakeBoxes[m,TraditionalForm],"/",MakeBoxes[n,TraditionalForm]}],"}"}]

Show[GraphicsArray[
Partition[Graphics[{Red,Polygram@@#},PlotLabel->TraditionalForm[label[#]],AspectRatio->Automatic]&/@Flatten[Table[{n,#}&/@Range[2,(n-1)/2],{n,3,12}],1],6]
],ImageSize->500]

V6

MakeBoxes[label[{m_,n_}],TraditionalForm]:=RowBox[{"{",RowBox[{MakeBoxes[m,TraditionalForm],"/",MakeBoxes[n,TraditionalForm]}],"}"}]

GraphicsGrid[
Partition[Graphics[{Red,Polygram@@#},PlotLabel->TraditionalForm[label[#]],AspectRatio->Automatic]&/@Flatten[Table[{n,#}&/@Range[2,(n-1)/2],{n,3,12}],1],6]
]