Triakis Icosahedral Graph

Author

Eric W. Weisstein
April 20, 2021

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

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

©2021 Wolfram Research, Inc. except for portions noted otherwise

Additional Authors

Nice planar embedding by Ed Pegg, Jr.

Graph

GraphData["TriakisIcosahedralGraph"]//StyleGraphs[#,VertexSize->{"Scaled",.02}]&

All

GraphData["TriakisIcosahedralGraph","Graph","All"]//StyleGraphs

Degenerate

GraphData["TriakisIcosahedralGraph","Graph","Degenerate"]//StyleGraphs

LCF

GraphData["TriakisIcosahedralGraph","Graph","LCF"]//StyleGraphs

MinimalCrossing

GraphData["TriakisIcosahedralGraph","Graph","MinimalCrossing"]//StyleGraphs

Perspective

GraphData["TriakisIcosahedralGraph","Graph","Perspective"]//StyleGraphs

Planar

GraphData["TriakisIcosahedralGraph","Graph","Planar"]//StyleGraphs

UnitDistance

GraphData["TriakisIcosahedralGraph","UnitDistance"]

GraphData["TriakisIcosahedralGraph","Graph","UnitDistance"]//StyleGraphs

3D

GraphData["TriakisIcosahedralGraph","Graph","3D"]

Embeddings

GraphDataEmbeddings[GraphData["TriakisIcosahedralGraph","EdgeList"]]

Perspective projection

PolyhedronProjectionGraph[PolyhedronData["TriakisIcosahedron","Polyhedron"],#,"Simplification"->FullSimplify]&/@{{0,1,0,-ArcTan[(1/2)-((Sqrt[5])/2)]},
{1,(1/61) (Sqrt[2885-1102 (Sqrt[5])]),(1/61) (17+3 (Sqrt[5])),ArcTan[(1/4) (NumericalApproximation[Root, (RowDefault["1.52", FEExpressionsNumericalApproximationElider]), Root[145-65 ((#1)^2)+((#1)^4)&,3], ])]},
{1,(1/29) (Sqrt[1765-722 (Sqrt[5])]),-(3/29) (-11+(Sqrt[5])),ArcTan[4 (Sqrt[(2/(285+127 (Sqrt[5])))])]},
{1,(NumericalApproximation[Root, (RowDefault["0.375", FEExpressionsNumericalApproximationElider]), Root[605-4325 ((#1)^2)+121 ((#1)^4)&,3], ]),(1/2) (-1+(Sqrt[5])),-ArcTan[(Sqrt[(1/85) (25-2 (Sqrt[5]))])]},
{1,0,-(1/11) (13-5 (Sqrt[5]))},
{1,0,(1/61) (17+3 (Sqrt[5]))},
{1,0,(1/4) (3-(Sqrt[5]))},
{1,(Sqrt[5-2 (Sqrt[5])]),(1/2) (-1+(Sqrt[5])),-ArcCot[(Sqrt[85+38 (Sqrt[5])])]}}

GraphData["TriakisIcosahedralGraph","Graph","Perspective"]

Stereographic projection

PolyhedronData[poly]

Degenerate

Manipulate[GraphPlot[SkeletonGraph[PolyhedronData[poly,"Faces"]//Normal,r],Method->None],{r,.1,10}]

GraphPlot[SkeletonGraph[PolyhedronData[poly,"Faces"]//Normal,#],Method->None]&/@{1.9,2.7,3,3.5,5,6}

rs=RecognizeGraph/@(gs=ToCombinatoricaGraph/@{})

ToCommonEdges[#,rs[[1]]]&/@gs

Properties

Classes

GraphData[g,"Classes"]

Matrices

GraphicsRow[GraphMatrixPlot[GraphData["TriakisIcosahedralGraph"]]]

Properties

GraphData[g,"Missing"]

GraphData[g,{"V","M"}]

TableForm[GraphDataTable[g,x],TableDepth->2]//TraditionalForm

GraphData

GraphClasses

GraphClassString[g]