Pentakis Icosidodecahedral Graph

Author

Eric W. Weisstein
September 1, 2022

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

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

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

Embeddings

GraphData["PentakisIcosidodecahedralGraph","StandardName"]

Construction (LiPonomarenkoZemanGraph)

Import["https://arxiv.org/pdf/2305.17302v1.pdf",{"PageGraphics",19}]

Column[Row/@Map[Show[GraphData["LiPonomarenkoZemanGraph"<>#],PlotLabel->#]&,{{"X10","X18","X20","X32"},{"Y42","X48","Y50"},{"X42","X50"}},{2}],Alignment->Center]

Primary

GraphData["PentakisIcosidodecahedralGraph"]//StyleGraphs[#,ImageSize->Small,VertexSize->{"Scaled",.015}]&

All

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

Planar

GraphData["PentakisIcosidodecahedralGraph","Planar"]

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

MinimalCrossing

GraphData["PentakisIcosidodecahedralGraph",{"RCN","CN"}]

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

MinimalCrossing construction

g=RotateGraph[MinimalCrossingGraph[GraphData["PentakisIcosidodecahedralGraph"],"CrossingNumber"->-1]]

RectilinearCrossingCount[g]

Tutte embeddings

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

Tally[ReverseSort[Length/@faces]]

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

gs=Annotate[#,{VertexLabels->None,ImageSize->Tiny}]&/@{,RotateGraph[,2Pi/3]}

Tutte embedding construction 3 #1

GraphPlot[g=RotateGraph[,2Pi/3]]

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

RecognizeGraph[g]

Tutte embedding construction 3 #2

GraphPlot[RotateGraph[]]

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

RecognizeGraph[g]

Circular

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

Halin

GraphData["PentakisIcosidodecahedralGraph","Halin"]

GraphData["PentakisIcosidodecahedralGraph","Graph","Halin"]//StyleGraphs

LCF

GraphData["PentakisIcosidodecahedralGraph","LCF"]

GraphData["PentakisIcosidodecahedralGraph","Regular"]

GraphData["PentakisIcosidodecahedralGraph","LCFSignature"]

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

UnitDistance

GraphData["PentakisIcosidodecahedralGraph","UnitDistance"]

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

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

Matchstick

GraphData["PentakisIcosidodecahedralGraph","Matchstick"]

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

Default embedding

g=Graph@GraphData["PentakisIcosidodecahedralGraph","Edges"]

RecognizeGraph[g]

3D default

Graph3D[GraphData["PentakisIcosidodecahedralGraph","Edges"]]

3D All

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

3D UnitDistance

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

3D Polyhedron

GraphData["PentakisIcosidodecahedralGraph","Polyhedral"]

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

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

3D Canonical

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

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

3D Canonical from solid

g=PolyhedronGraph[PolyhedronData["PentakisIcosidodecahedron","Polyhedron"]/.Polyhedron[v_,f_]:>FullSimplify@Polyhedron[v/PolyhedronData["PentakisIcosidodecahedron","Midradius"],f]]

RecognizeGraph[g]

Properties

PolyhedralEmbeddings

GraphData["PentakisIcosidodecahedralGraph","PolyhedralEmbeddings"]

GraphData

GraphDataClassString

GraphDataClassString["PentakisIcosidodecahedralGraph"]

GraphDataString

file=OpenWrite["~/pig.m"]

WriteString[file,GraphDataString[
g,
"StandardName"->"PentakisIcosidodecahedralGraph",
"Name"->"pentakis icosidodecahedral graph",
"Information"->"PentakisIcoidodecahedralGraph"
]]

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