Disdyakis Triacontahedral Graph

Author

Eric W. Weisstein
September 16, 2022

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

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

©2022 Wolfram Research, Inc. except for portions noted otherwise

Graph

Primary

GraphData["DisdyakisTriacontahedralGraph"]//StyleGraphs[#,ImageSize->Small]&

All

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

Default embedding

GraphPlot@GraphData["DisdyakisTriacontahedralGraph","Edges"]

v={};
g=Graph[Range[Length[v]],UndirectedEdge@@@{},VertexCoordinates->v,VertexLabels->Automatic]

RecognizeGraph[g]

Degenerate

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

Circular

GraphData["DisdyakisTriacontahedralGraph","Graph","Circular"]//StyleGraphs

Planar

GraphData["DisdyakisTriacontahedralGraph","Planar"]

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

Tutte embeddings

faces=ReverseSort@SymmetricallyDistinctFaces[GraphData["DisdyakisTriacontahedralGraph"]]

Tally[ReverseSort[Length/@faces]]

IGLayoutTutte[GraphData["DisdyakisTriacontahedralGraph"],"OuterFace"->#]&/@faces

gs=Annotate[#,{VertexLabels->None,ImageSize->Tiny}]&/@{}

RecognizeGraph/@gs

Tutte embedding construction

GraphPlot[RotateGraph[,2Pi/3]]

v=Join[];
g=Graph[Range[Length[v]],UndirectedEdge@@@{},VertexCoordinates->v,VertexLabels->Automatic]

RecognizeGraph[g]

LCF

GraphData["DisdyakisTriacontahedralGraph","LCF"]

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

Perspective

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

UnitDistance

GraphData["DisdyakisTriacontahedralGraph","UnitDistance"]

UnitDistanceGraphQ[GraphData["DisdyakisTriacontahedralGraph"],Debug->True]//Timing

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

Embeddings

GraphDataEmbeddings[GraphData["DisdyakisTriacontahedralGraph","EdgeList"]]

Matchstick

GraphData["DisdyakisTriacontahedralGraph","Matchstick"]

GraphData["DisdyakisTriacontahedralGraph","Graph","Matchstick"]//StyleGraphs

3D default

Graph3D[GraphData["DisdyakisTriacontahedralGraph","Edges"]]

3D All

GraphData["DisdyakisTriacontahedralGraph","Graph",{"3D","All"}]

3D UnitDistance

GraphData["DisdyakisTriacontahedralGraph","Graph",{"3D","UnitDistance"}]

3D Polyhedron

GraphData["DisdyakisTriacontahedralGraph","Polyhedral"]

GraphData["DisdyakisTriacontahedralGraph","Graph",{"3D","Polyhedron"}]

Graphics3D[{FaceForm[Green,Red],GraphData["DisdyakisTriacontahedralGraph","Polyhedron"]}]

3D Canonical

GraphData["DisdyakisTriacontahedralGraph","Graph",{"3D","Canonical"}]

Graphics3D[{Opacity[.5],Red,GraphData["DisdyakisTriacontahedralGraph","Polyhedron","Canonical"],Yellow,Sphere[]}]

Perspective projections

PolyhedronProjectionGraph[PolyhedronData["DisdyakisTriacontahedron","Polyhedron"],#,"Simplification"->FullSimplify]&/@{{(1/2) (-1+(Sqrt[5])),1,(1/2) (3-(Sqrt[5])),-ArcTan[(3/2)-((Sqrt[5])/2)]},{(1/8) (9-(Sqrt[5])),1,0},{1,(1/278) (-19+129 (Sqrt[5])),(5/278) (-17+13 (Sqrt[5])),-ArcCot[(3/(Sqrt[1630-728 (Sqrt[5])]))]},{(1/10) (-5+3 (Sqrt[5])),(1/10) (5-(Sqrt[5])),1,ArcTan[(NumericalApproximation[Root, (RowDefault["0.588", FEExpressionsNumericalApproximationElider]), Root[5-20 ((#1)^2)+16 ((#1)^4)&,3], ])]},{1,1,0},{1,1,1,π/2-ArcCot[(Sqrt[3 (9+4 (Sqrt[5]))])]},{1,(1/2) (-1+(Sqrt[5])),0}}

GraphData["DisdyakisTriacontahedralGraph","Graph","Perspective"]

Properties

Classes

GraphData[g,"Classes"]

Matrices

GraphicsRow[GraphMatrixPlot[GraphData["DisdyakisTriacontahedralGraph"]]]

Properties

GraphData[g,"Missing"]

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

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

Embeddings by Projection

PolyhedronData[poly]

GraphPlot[SkeletonGraph[PolyhedronData[poly,"Faces"]//Normal,#],Method->None]&/@{.5,1,2,3,5}

GraphData

GraphClasses

GraphClassString[g]