Deltoidal Hexecontahedral Graph

Author

Eric W. Weisstein
April 29, 2021

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

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

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

Graph

All

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

Degenerate

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

LCF

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

GraphData["DeltoidalHexecontahedralGraph","LCF"]

MinimalCrossing

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

Perspective

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

Planar

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

UnitDistance

GraphData["DeltoidalHexecontahedralGraph","UnitDistance"]

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

3-D

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

Embeddings

GraphDataEmbeddings[GraphData["DeltoidalHexecontahedralGraph","EdgeList"]]

Perspective projections

PolyhedronProjectionGraph[PolyhedronData["DeltoidalHexecontahedron","Polyhedron"],#,"Simplification"->FullSimplify]&/@{{0,1,0},{1,1,1,-ArcCot[(Sqrt[3 (9+4 (Sqrt[5]))])]},{-(5/6) (-3+(Sqrt[5])),(1/6) (-11+7 (Sqrt[5])),1,-ArcCot[(Sqrt[(1/202) (331+50 (Sqrt[5]))])]},{1,0,1},{0,(1/11) (7+(Sqrt[5])),1},{0,(1/2) (-1+(Sqrt[5])),1},{1,(1/2) (-1+(Sqrt[5])),0,π/2}}

GraphData["DeltoidalHexecontahedralGraph","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

From Ed Pegg

pers. comm.
Dec 21, 2009

l=Graphics[Line/@{{{10,6},{11,5}},{{16,8},{8,16}},{{8,16},{0,8}},{{8,13},{8,16}},{{5,12},{8,13}},{{11,12},{8,13}},{{8,12},{8,13}},{{9,12},{8,12}},{{8,12},{7,12}},{{9,12},{10,11}},{{11,12},{9,12}},{{7,12},{6,11}},{{5,12},{7,12}},{{8,11},{9,12}},{{8,11},{7,12}},{{8,0},{0,8}},{{8,0},{16,8}},{{8,0},{10,3}},{{8,0},{6,3}},{{10,3},{12,5}},{{10,3},{11,5}},{{9,3},{10,3}},{{10,4},{9,3}},{{8,3},{9,3}},{{8,3},{7,3}},{{6,3},{5,5}},{{6,3},{4,5}},{{7,3},{6,3}},{{6,4},{7,3}},{{8,3},{8,0}},{{8,3},{8,3}},{{8,4},{8,3}},{{10,4},{11,5}},{{8,4},{10,4}},{{6,4},{8,4}},{{6,4},{5,5}},{{6,5},{6,4}},{{6,5},{7,5}},{{6,6},{6,5}},{{10,5},{9,5}},{{10,5},{10,4}},{{10,6},{10,5}},{{7,5},{7,6}},{{8,4},{7,5}},{{9,5},{9,6}},{{8,4},{9,5}},{{8,5},{9,5}},{{8,5},{7,5}},{{9,11},{8,11}},{{8,11},{7,11}},{{8,10},{8,11}},{{9,11},{10,11}},{{9,10},{9,11}},{{8,10},{9,10}},{{7,10},{8,10}},{{7,11},{7,10}},{{6,11},{7,11}},{{11,11},{10,11}},{{5,11},{6,11}},{{9,9},{9,10}},{{7,9},{7,10}},{{11,12},{11,11}},{{5,12},{5,11}},{{0,8},{5,12}},{{16,8},{11,12}},{{11,5},{12,7}},{{5,5},{4,7}},{{6,9},{7,11}},{{10,9},{9,11}},{{11,5},{11,9}},{{5,5},{5,9}},{{6,7},{6,6}},{{10,7},{10,6}},{{9,6},{10,8}},{{7,6},{6,8}},{{12,7},{11,12}},{{11,10},{11,11}},{{9,9},{10,9}},{{10,9},{11,11}},{{11,9},{10,9}},{{10,9},{10,8}},{{6,9},{6,8}},{{5,9},{6,9}},{{6,9},{5,11}},{{7,9},{6,9}},{{5,10},{5,11}},{{4,7},{5,12}},{{12,5},{16,8}},{{4,5},{0,8}},{{4,7},{4,5}},{{5,10},{4,7}},{{5,9},{5,10}},{{8,10},{8,10}},{{8,9},{8,10}},{{8,9},{9,7}},{{7,7},{8,9}},{{8,9},{9,9}},{{7,9},{8,9}},{{9,6},{10,6}},{{6,6},{5,5}},{{7,6},{6,6}},{{8,6},{8,5}},{{8,6},{9,6}},{{8,6},{7,6}},{{8,7},{8,6}},{{9,7},{9,6}},{{7,7},{7,6}},{{9,8},{9,9}},{{7,8},{7,9}},{{12,7},{12,5}},{{11,10},{12,7}},{{11,9},{11,10}},{{10,7},{11,9}},{{10,8},{10,7}},{{9,8},{10,8}},{{9,7},{9,8}},{{8,7},{9,7}},{{7,7},{8,7}},{{7,8},{7,7}},{{6,8},{7,8}},{{6,7},{6,8}},{{5,9},{6,7}}}];

RecognizeGraph[g=LinesToGraph[l,.1]]

GraphPlot[g,Method->None]

v=ToCommonEdges[g,Graph["DeltoidalHexecontahedralGraph"]]

List@@@PolyhedronData["RhombicHexecontahedron","SkeletonRules"]

ToCommonEdges[ChangeVertices[Graph["DeltoidalHexecontahedralGraph"],v],FromUnorderedPairs[PolyhedronData["RhombicHexecontahedron","EdgeIndices"]]]

ToCommonEdges[ChangeVertices[Graph["DeltoidalHexecontahedralGraph"],v],FromUnorderedPairs[PolyhedronData["DeltoidalHexecontahedron","EdgeIndices"]]]

GetGraphData["DeltoidalHexecontahedralGraph","File"]

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]