Simple Polyhedron

Author

Eric W. Weisstein
March 1, 2009

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

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

©2009 Wolfram Research, Inc. except for portions noted otherwise

Code

SimplePolyhedra[n_]:=Select[PlanarGraphs[n],V[#]>2&&M[#]==3n-6&]

Enumeration

Length/@(simple=SimplePolyhedra/@Range[9])//Timing

Table[KConnectedQ[3,#]&/@simple[i],{i,7}]

V5

ShowGraphArray[
DeleteCases[Take[simple,7],{}],
VertexStyle->Disk[.12]
]

V6

l=Function[n,Select[GraphData["Planar",n],GraphData[#,"E"]==3n-6&]]/@Range[7]

GraphicsGrid[Map[GraphPlot[Graph[#],Method->None,BaseStyle->Italic,PlotLabel->TextCell[GraphData[#,"Name"],PageWidth->80,TextAlignment->Center]]&,Drop[l,2],{2}],ImageSize->400,Spacings->{-30,30}]