Pentakis Dodecahedral Graph

Author

Eric W. Weisstein
April 30, 2021

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

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

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

Graph

All

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

Degenerate

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

LCF

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

MinimalCrossing

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

Perspective

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

Planar

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

UnitDistance

GraphData["PentakisDodecahedralGraph","UnitDistance"]

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

3-D

GraphData["PentakisDodecahedralGraph","Graph","3D"]//StyleGraphs

Embeddings

GraphDataEmbeddings[GraphData["PentakisDodecahedralGraph","EdgeList"]]

Perspective projections

PolyhedronProjectionGraph[PolyhedronData["PentakisDodecahedron","Polyhedron"],#,"Simplification"->FullSimplify]&/@{{0,1,0,-ArcTan[(1/2) (-1+(Sqrt[5]))]},{1,(Sqrt[5-2 (Sqrt[5])]),-(1/11) (13-5 (Sqrt[5])),ArcTan[(Sqrt[30])]},{-1/2,0,1},{-1/2,.11,1},{1,(Sqrt[5-2 (Sqrt[5])]),-2+(Sqrt[5]),-ArcTan[(Sqrt[15])]},{1,(Sqrt[5-2 (Sqrt[5])]),-(1/2) (-1+(Sqrt[5])),-ArcCot[3 (Sqrt[1+(2/(Sqrt[5]))])]}}

GraphData["PentakisDodecahedralGraph","Graph","Perspective"]

Properties

Classes

GraphData[g,"Classes"]

Matrices

GraphDataMatrices[g]

Properties

GraphData[g,"Missing"]

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

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

Embeddings by Projection

PolyhedronData[poly]

Degenerate

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

GraphData

GraphClasses

GraphClassString[g]