Snub Dodecadodecahedral Graph

Author

Eric W. Weisstein
May 7, 2026

This notebook downloaded from https://mathworld.wolfram.com/notebooks/GraphTheory/SnubDodecadodecahedralGraph.nb.

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

©2026 Wolfram Research, Inc. except for portions noted otherwise

Figures

GraphicsRow[
StyleGraphs[
GraphData["SnubDodecadodecahedralGraph","Graph","All"],
{ImageSize->300,VertexSize->{"Scaled",.02}}
],
Dividers->All
]

Embeddings

<<MathWorld`Graphs`

Names

GraphData["SnubDodecadodecahedralGraph","StandardName"]

GraphData["SnubDodecadodecahedralGraph","StandardNames"]

HouseOfGraphs

hogid=GraphData["SnubDodecadodecahedralGraph","NotationRules","HouseOfGraphs"]

HouseOfGraphsLookup[hogid]

HouseOfGraphsGraph[hogid]//StyleGraphs[#,ImageSize->Small]&

Wikidata

GraphData["SnubDodecadodecahedralGraph","WikidataID"]

GraphData["SnubDodecadodecahedralGraph","WikidataID","URL"]

Primary

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

All

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

CurvedEdge

GraphData["SnubDodecadodecahedralGraph","Graph","CurvedEdge"]//StyleGraphs

Inexact

Select[GraphData["SnubDodecadodecahedralGraph","Graph","All"],(!FreeQ[GraphEmbedding[#],_?InexactNumberQ]&)]//StyleGraphs

Embedding types

GraphDataEmbeddings[GraphData["SnubDodecadodecahedralGraph","EdgeList"]]

Default embedding

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

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

RecognizeGraph[g]

Degenerate

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

DegenerateGraphEmbeddingTypes/@GraphData["SnubDodecadodecahedralGraph","Graph","Degenerate"]

Perspective

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

Perspective construction

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

Manipulate[PolyhedronProjectionGraph[GraphData["SnubDodecadodecahedralGraph","Polyhedron"],{x,y,z}],{x,-1,1},{y,-1,1},{z,-1,1}]

PolyhedronProjectionGraph[GraphData["SnubDodecadodecahedralGraph","Polyhedron"],{0,.01,.01}]

PolyhedronProjectionGraph[GraphData["SnubDodecadodecahedralGraph","Polyhedron"],{0,0,1}]

PolyhedronProjectionGraph[GraphData["SnubDodecadodecahedralGraph","Polyhedron"],{0,1,0}]

PolyhedronProjectionGraph[GraphData["SnubDodecadodecahedralGraph","Polyhedron"],{1,0.01,0}]

PolyhedronProjectionGraph[GraphData["SnubDodecadodecahedralGraph","Polyhedron"],{1,1,0}]

PolyhedronProjectionGraph[GraphData["SnubDodecadodecahedralGraph","Polyhedron"],{1,0,1,-Pi/2}]

PolyhedronProjectionGraph[GraphData["SnubDodecadodecahedralGraph","Polyhedron"],{1,1,1}]

Bilateral

GraphData["SnubDodecadodecahedralGraph","Graph","Bilateral"]//StyleGraphs

Circular

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

Planar

GraphData["SnubDodecadodecahedralGraph","Planar"]

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

MinimalCrossingNumber crossings.uos.de

CrossingNumber[GraphData["SnubDodecadodecahedralGraph"],Method->"WebCompute"]//AbsoluteTiming

DateString[]

MinimalCrossingNumber: "EmbeddingScheme" -> 1

(cn=CrossingNumber[GraphData["SnubDodecadodecahedralGraph"],"EmbeddingScheme"->1,TimeConstraint->1])//AbsoluteTiming

(cn=CrossingNumber[GraphData["SnubDodecadodecahedralGraph"],"EmbeddingScheme"->1,TimeConstraint->10])//AbsoluteTiming

(cn=CrossingNumber[GraphData["SnubDodecadodecahedralGraph"],"EmbeddingScheme"->1,TimeConstraint->60])//AbsoluteTiming

(cn=CrossingNumber[GraphData["SnubDodecadodecahedralGraph"],"EmbeddingScheme"->1,TimeConstraint->3600])//AbsoluteTiming

(cn=CrossingNumber[GraphData["SnubDodecadodecahedralGraph"],"EmbeddingScheme"->1,TimeConstraint->5 3600])//AbsoluteTiming

(cn=CrossingNumber[GraphData["SnubDodecadodecahedralGraph"],"EmbeddingScheme"->1,TimeConstraint->86400])//AbsoluteTiming

MinimalCrossingNumber: "EmbeddingScheme" -> 2

(cn=CrossingNumber[GraphData["SnubDodecadodecahedralGraph"],"EmbeddingScheme"->2,TimeConstraint->1])//AbsoluteTiming

(cn=CrossingNumber[GraphData["SnubDodecadodecahedralGraph"],"EmbeddingScheme"->2,TimeConstraint->10])//AbsoluteTiming

(cn=CrossingNumber[GraphData["SnubDodecadodecahedralGraph"],"EmbeddingScheme"->2,TimeConstraint->60])//AbsoluteTiming

(cn=CrossingNumber[GraphData["SnubDodecadodecahedralGraph"],"EmbeddingScheme"->2,TimeConstraint->3600])//AbsoluteTiming

(cn=CrossingNumber[GraphData["SnubDodecadodecahedralGraph"],"EmbeddingScheme"->2,TimeConstraint->5 3600])//AbsoluteTiming

(cn=CrossingNumber[GraphData["SnubDodecadodecahedralGraph"],"EmbeddingScheme"->2,TimeConstraint->86400])//AbsoluteTiming

MinimalCrossingNumber: "EmbeddingScheme" -> 3

(cn=CrossingNumber[GraphData["SnubDodecadodecahedralGraph"],"EmbeddingScheme"->3,TimeConstraint->1])//AbsoluteTiming

(cn=CrossingNumber[GraphData["SnubDodecadodecahedralGraph"],"EmbeddingScheme"->3,TimeConstraint->10])//AbsoluteTiming

(cn=CrossingNumber[GraphData["SnubDodecadodecahedralGraph"],"EmbeddingScheme"->3,TimeConstraint->60])//AbsoluteTiming

(cn=CrossingNumber[GraphData["SnubDodecadodecahedralGraph"],"EmbeddingScheme"->3,TimeConstraint->3600])//AbsoluteTiming

(cn=CrossingNumber[GraphData["SnubDodecadodecahedralGraph"],"EmbeddingScheme"->3,TimeConstraint->5 3600])//AbsoluteTiming

(cn=CrossingNumber[GraphData["SnubDodecadodecahedralGraph"],"EmbeddingScheme"->3,TimeConstraint->86400])//AbsoluteTiming

Quit

MinimalCrossing

GraphData["SnubDodecadodecahedralGraph","CN"]

(gs=GraphData["SnubDodecadodecahedralGraph","Graph","MinimalCrossing"])//StyleGraphs

GraphCrossingCount/@gs

GraphCrossingDiagram/@gs

MinimalRectilinearCrossing

GraphData["SnubDodecadodecahedralGraph","RCN"]

GraphData["SnubDodecadodecahedralGraph","Graph","MinimalRectilinearCrossing"]//StyleGraphs

MinimalCrossing construction Tutte

cn=160;

(g=MinimalCrossingGraph[GraphData["SnubDodecadodecahedralGraph"],"CrossingNumber"->cn])//PolyhedralGraphQ//AbsoluteTiming

faces=ReverseSort@SymmetricallyDistinctFaces[g]

Tally[ReverseSort[Length/@faces]]

TutteGraphs=BilateralGraph[CenterGraph@IGLayoutTutte[g,"OuterFace"->#],"ReturnNonbilateralGraph"->True]&/@faces

TutteGraphsWithOuterCrossingPointCounts={
#,
Count[OuterFace[#],_?(GreaterThan[GraphData["SnubDodecadodecahedralGraph","V"]])]
}&/@TutteGraphs;

Cases[TutteGraphsWithOuterCrossingPointCounts,{g_,0}:>g]

Cases[TutteGraphsWithOuterCrossingPointCounts,{g_,1}:>g]

LocalCrossingNumberWithEmbeddings=
{1+Max[Length/@DeleteCases[
Drop[AdjacencyList[#],GraphData["SnubDodecadodecahedralGraph","V"]],
_Integer?(LessEqualThan[GraphData["SnubDodecadodecahedralGraph","V"]]),
{2}
]],#}&/@TutteGraphs

TutteGraphsWithSymmetryGroups={
#,
GraphSymmetryGroup[
#,
AdditionalData->Join[Table[True,GraphData["SnubDodecadodecahedralGraph","V"]],Table[False,cn]],
SameTest->Equal
]
}&/@TutteGraphs;

SymmetricEmbeddingsWithOrientations=DeleteCases[
TutteGraphsWithSymmetryGroups,
{_,TransformationGroup[{}]}
]

Select[SymmetricEmbeddingsWithOrientations[[All,1]],Count[OuterFace[#],_?(GreaterThan[GraphData["SnubDodecadodecahedralGraph","V"]])]==0&]

MinimalCrossing construction Random 1k [XXX s]

(cn=CrossingNumber[GraphData["SnubDodecadodecahedralGraph"],TimeConstraint->1])//AbsoluteTiming

Length[diagrams=DistinctMinimalCrossingDiagramData[
GraphData["SnubDodecadodecahedralGraph"],
1000,
"CrossingNumber"->cn,
EdgeShapeFunction->"BezierEdge"
]]//AbsoluteTiming

No crossing points on the boundary:

Length[diagrams0=Lookup[Select[diagrams,MinimalCrossingOuterCrossingCount[#]==0&],"Graph",{}]//Timing

One crossing point on the boundary:

Length[diagrams1=Lookup[Select[diagrams,MinimalCrossingOuterCrossingCount[#]==1&],"Graph",{}]]//Timing

graphs=#["Graph"]&/@diagrams;

Symmetric embeddings:

RandomGraphsWithSymmetryGroups={
#,
GraphSymmetryGroup[#]
}&/@graphs;//AbsoluteTiming

MaxMemoryUsed[]/10^9.GB

Symmetric embeddings:

Length[SymmetricMinimalEmbeddingData=DeleteCases[
RandomGraphsWithSymmetryGroups,
{_,TransformationGroup[{}]}
]
]//AbsoluteTiming

SymmetricMinimalEmbeddingData

SymmetricMinimalEmbeddingGraphs=SymmetricMinimalEmbeddingData[[All,1]]

GraphCrossingCount/@SymmetricMinimalEmbeddingGraphs

GraphCrossingDiagram/@SymmetricMinimalEmbeddingGraphs

MinimalCrossing construction Random 5k [XXX s]

(cn=CrossingNumber[GraphData["SnubDodecadodecahedralGraph"],TimeConstraint->1])//AbsoluteTiming

Length[diagrams=DistinctMinimalCrossingDiagramData[
GraphData["SnubDodecadodecahedralGraph"],
51000,
"CrossingNumber"->cn,
EdgeShapeFunction->"BezierEdge"
]]//AbsoluteTiming

No crossing points on the boundary:

Length[diagrams0=Lookup[Select[diagrams,MinimalCrossingOuterCrossingCount[#]==0&],"Graph",{}]]//Timing

One crossing point on the boundary:

Length[diagrams1=Lookup[Select[diagrams,MinimalCrossingOuterCrossingCount[#]==1&],"Graph",{}]]//Timing

graphs=#["Graph"]&/@diagrams;

Symmetric embeddings:

RandomGraphsWithSymmetryGroups={
#,
GraphSymmetryGroup[#]
}&/@graphs;//AbsoluteTiming

MaxMemoryUsed[]/10^9.GB

Symmetric embeddings:

Length[SymmetricMinimalEmbeddingData=DeleteCases[
RandomGraphsWithSymmetryGroups,
{_,TransformationGroup[{}]}
]
]//AbsoluteTiming

SymmetricMinimalEmbeddingData

SymmetricMinimalEmbeddingGraphs=SymmetricMinimalEmbeddingData[[All,1]]

GraphCrossingCount/@SymmetricMinimalEmbeddingGraphs

GraphCrossingDiagram/@SymmetricMinimalEmbeddingGraphs

MinimalCrossing construction Random 20k [XXX s]

(cn=CrossingNumber[GraphData["SnubDodecadodecahedralGraph"],TimeConstraint->1])//AbsoluteTiming

Length[diagrams=DistinctMinimalCrossingDiagramData[
GraphData["SnubDodecadodecahedralGraph"],
20*^3,
"CrossingNumber"->cn,
EdgeShapeFunction->"BezierEdge"
]]//AbsoluteTiming

No crossing points on the boundary:

Length[diagrams0=Lookup[Select[diagrams,MinimalCrossingOuterCrossingCount[#]==0&],"Graph",{}]]//Timing

One crossing point on the boundary:

Length[diagrams1=Lookup[Select[diagrams,MinimalCrossingOuterCrossingCount[#]==1&],"Graph",{}]]//Timing

graphs=#["Graph"]&/@diagrams;

Symmetric embeddings:

RandomGraphsWithSymmetryGroups={
#,
GraphSymmetryGroup[#]
}&/@graphs;//AbsoluteTiming

MaxMemoryUsed[]/10^9.GB

Symmetric embeddings:

Length[SymmetricMinimalEmbeddingData=DeleteCases[
RandomGraphsWithSymmetryGroups,
{_,TransformationGroup[{}]}
]
]//AbsoluteTiming

SymmetricMinimalEmbeddingData

SymmetricMinimalEmbeddingGraphs=SymmetricMinimalEmbeddingData[[All,1]]

GraphCrossingCount/@SymmetricMinimalEmbeddingGraphs

GraphCrossingDiagram/@SymmetricMinimalEmbeddingGraphs

MinimalCrossing construction Random 1k [old]

(cn=CrossingNumber[GraphData["SnubDodecadodecahedralGraph"],TimeConstraint->1])//AbsoluteTiming

(RandomGraphs=Table[MinimalCrossingGraph[GraphData["SnubDodecadodecahedralGraph"],"CrossingNumber"->cn,RandomSeed->n],{n,1000}]//Union);//Timing

RandomGraphsWithOuterCrossingPointCounts={
#,
Count[OuterFace[#],_?(GreaterThan[GraphData["SnubDodecadodecahedralGraph","V"]])]
}&/@RandomGraphs;

Small numbers of crossing points on the boundary:

Cases[RandomGraphsWithOuterCrossingPointCounts,{g_,0}:>g]

Cases[RandomGraphsWithOuterCrossingPointCounts,{g_,1}:>g]

Symmetric embeddings:

RandomGraphsWithSymmetryGroups={
#,
GraphSymmetryGroup[
#,
AdditionalData->Join[Table[True,GraphData["SnubDodecadodecahedralGraph","V"]],Table[False,cn]],
SameTest->Equal
]
}&/@RandomGraphs;

MaxMemoryUsed[]/10^9.GB

DeleteCases[
RandomGraphsWithSymmetryGroups,
{_,TransformationGroup[{}]}
]/.g_Graph:>BilateralGraph[CenterGraph@g,"ReturnNonbilateralGraph"->True]

MinimalCrossing construction Random 20k [old]

(cn=CrossingNumber[GraphData["SnubDodecadodecahedralGraph"],TimeConstraint->1])//AbsoluteTiming

(RandomGraphs=Table[MinimalCrossingGraph[GraphData["SnubDodecadodecahedralGraph"],"CrossingNumber"->cn,RandomSeed->n],{n,20000}]//Union);//Timing

RandomGraphsWithOuterCrossingPointCounts={
#,
Count[OuterFace[#],_?(GreaterThan[GraphData["SnubDodecadodecahedralGraph","V"]])]
}&/@RandomGraphs;

Small numbers of crossing points on the boundary:

Cases[RandomGraphsWithOuterCrossingPointCounts,{g_,0}:>g]

Cases[RandomGraphsWithOuterCrossingPointCounts,{g_,1}:>g]

Symmetric embeddings:

RandomGraphsWithSymmetryGroups={
#,
GraphSymmetryGroup[
#,
AdditionalData->Join[Table[True,GraphData["SnubDodecadodecahedralGraph","V"]],Table[False,cn]],
SameTest->Equal
]
}&/@RandomGraphs;

MaxMemoryUsed[]/10^9.GB

DeleteCases[
RandomGraphsWithSymmetryGroups,
{_,TransformationGroup[{}]}
]/.g_Graph:>BilateralGraph[CenterGraph@g,"ReturnNonbilateralGraph"->True]

MinimalLocalCrossing

GraphData["SnubDodecadodecahedralGraph",{"LocalCrossingNumber","RectilinearLocalCrossingNumber"}]

GraphData["SnubDodecadodecahedralGraph","Graph","MinimalLocalCrossing"]//StyleGraphs

MinimalRectilinearLocalCrossing

GraphData["SnubDodecadodecahedralGraph",{"LocalCrossingNumber","RectilinearLocalCrossingNumber"}]

GraphData["SnubDodecadodecahedralGraph","Graph","MinimalRectilinearLocalCrossing"]//StyleGraphs

MinimaRectilinearlLocalCrossing construction 1000

AdjacentCrossingsQ[g_Graph,cn_Integer]:=Module[{a=AdjacencyList[g],n=VertexCount[g]-cn},Max[Take[a,-cn]]>n]

(cn=CrossingNumber[GraphData["SnubDodecadodecahedralGraph"],TimeConstraint->10])//AbsoluteTiming

(gs=Select[Table[MinimalCrossingGraph[GraphData["SnubDodecadodecahedralGraph"],"CrossingNumber"->cn,RandomSeed->i],{i,1000}],!AdjacentCrossingsQ[#,cn]&]//Union)//Timing

MinimaRectilinearlLocalCrossing construction 20000

AdjacentCrossingsQ[g_Graph,cn_Integer]:=Module[{a=AdjacencyList[g],n=VertexCount[g]-cn},Max[Take[a,-cn]]>n]

(cn=CrossingNumber[GraphData["SnubDodecadodecahedralGraph"],TimeConstraint->10])//AbsoluteTiming

(gs=Select[Table[MinimalCrossingGraph[GraphData["SnubDodecadodecahedralGraph"],"CrossingNumber"->cn,RandomSeed->i],{i,20000}],!AdjacentCrossingsQ[#,cn]&]//Union)//Timing

Circulant

GraphData["SnubDodecadodecahedralGraph","Circulant"]

GraphData["SnubDodecadodecahedralGraph","Graph","Circulant"]//StyleGraphs

Line graph

GraphData["SnubDodecadodecahedralGraph","Line"]

LineGraphQ[GraphData["SnubDodecadodecahedralGraph"]]//Timing

RootGraph

Select[GraphData[All],GraphData[#,"LineGraph","Name"]=== "SnubDodecadodecahedralGraph"&]

RootGraph[GraphData["SnubDodecadodecahedralGraph"]]

Halin

GraphData["SnubDodecadodecahedralGraph","Halin"]

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

Rigid

GraphData["SnubDodecadodecahedralGraph","Rigid"]

GraphData["SnubDodecadodecahedralGraph","Graph","Rigid"]//StyleGraphs

Flexible

GraphData["SnubDodecadodecahedralGraph","Flexible"]

GraphData["SnubDodecadodecahedralGraph","Graph","Flexible"]//StyleGraphs

LCF

GraphData["SnubDodecadodecahedralGraph","LCF"]

GraphData["SnubDodecadodecahedralGraph","HamiltonianCycleCount"]

GraphData["SnubDodecadodecahedralGraph","LCFSignature"]

GraphData["SnubDodecadodecahedralGraph","LCFNotations"]

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

Tally[LCFNotation[#][[2]]&/@%]

LCF compute random

FindRandomLCFNotation[GraphData["SnubDodecadodecahedralGraph"],TimeConstraint->120]

LCF compute 10^5

Tally[(lcf=LCF[GraphData["SnubDodecadodecahedralGraph"],10^5])[[All,2]]]//Timing

MaxMemoryUsed[]/10.^9 "GB"

DeleteCases[lcf,{_,1}]

LCFGraph@@@DeleteCases[lcf,{_,1}]//StyleGraphs

(gs=Flatten[{
(* all LCF's with order >1, sorted by order and with bilateral graphs first *)
Join[DeleteCases[#,{_Missing,_}][[All,1]],Cases[#,{_Missing,_}][[All,2]]]&/@Map[{BilateralLCFGraph@#,#}&,Map[LCFGraph@@#&,SplitBy[DeleteCases[lcf,{_,1}],Last],{2}],{2}],
(* order-1 bilateral only *)
DeleteMissing[BilateralLCFGraph@@@Cases[lcf,{_,1}]]}])//Timing

Length[gs]

LCF compute 10^6

Tally[(lcf=LCF[GraphData["SnubDodecadodecahedralGraph"],10^6])[[All,2]]]//Timing

MaxMemoryUsed[]/10.^9 "GB"

DeleteCases[lcf,{_,1}]

LCFGraph@@@DeleteCases[lcf,{_,1}]//StyleGraphs

(gs=Flatten[{
(* all LCF's with order >1, sorted by order and with bilateral graphs first *)
Join[DeleteCases[#,{_Missing,_}][[All,1]],Cases[#,{_Missing,_}][[All,2]]]&/@Map[{BilateralLCFGraph@#,#}&,Map[LCFGraph@@#&,SplitBy[DeleteCases[lcf,{_,1}],Last],{2}],{2}],
(* order-1 bilateral only *)
DeleteMissing[BilateralLCFGraph@@@Cases[lcf,{_,1}]]}])//Timing

Length[gs]

LCF compute 10^7

Tally[(lcf=LCF[GraphData["SnubDodecadodecahedralGraph"],10^7])[[All,2]]]//Timing

MaxMemoryUsed[]/10.^9 "GB"

DeleteCases[lcf,{_,1}]

LCFGraph@@@DeleteCases[lcf,{_,1}]//StyleGraphs

(gs=Flatten[{
(* all LCF's with order >1, sorted by order and with bilateral graphs first *)
Join[DeleteCases[#,{_Missing,_}][[All,1]],Cases[#,{_Missing,_}][[All,2]]]&/@Map[{BilateralLCFGraph@#,#}&,Map[LCFGraph@@#&,SplitBy[DeleteCases[lcf,{_,1}],Last],{2}],{2}],
(* order-1 bilateral only *)
DeleteMissing[BilateralLCFGraph@@@Cases[lcf,{_,1}]]}])//Timing

Length[gs]

LCF compute ssham_lcf

l1={
{"SnubDodecadodecahedralGraph",{0,sig}}
};

PropertyReplace[l1,"LCFSignature"]

RenameGraphFiles[]

ReverseSort@Tally[(lcf=Import[FileNameJoin[{$GraphDataDirectory,"Properties","LCFNotations-Nice",GraphNameToFileName["SnubDodecadodecahedralGraph",".m.gz"]}]])[[All,2]]]

lcf={
{{{-30,-29,-21},{-25,-24,29},{-26,-6,26},{-14,-7,25},{-15,17,18},{-20,-19,-16},{-21,25,26},{6,15,24},{-15,-14,5},{-16,20,21},{-23,-22,19},{-24,13,14},{2,3,12},{-6,-5,9},{-19,-18,-2},{-3,20,21},{-30,-29,19},{23,24,29},{2,3,22},{14,15,16},{-2,7,8},{-17,-3,2},{-18,-15,-9},{-2,15,16},{-13,-12,14},{-14,2,19},{6,7,18},{-7,-2,2},{-26,-25,-8},{-20,-19,-2}},2},
{{{-30,-29,-25},{16,26,29},{-26,-25,15},{-26,18,19},{-24,2,18},{7,24,25},{-26,-2,26},{2,25,26},{8,17,18},{-2,2,7},{-15,24,26},{-16,-2,3},{-7,2,17},{-24,9,10},{-29,-3,-2},{-30,3,29},{-8,-7,2},{-16,-15,10},{-3,-2,3},{-26,2,24},{-24,-23,-22},{-18,-3,-2},{-19,-18,-9},{-25,-10,26},{-26,-25,2},{-17,15,16},{-18,-2,24},{-26,-10,23},{22,25,26},{-24,-17,25}},2}

};

gs=NiceLCFGraphs[lcf,2]

Length[gs]

nicelcf=LCFNotation/@gs

l2={
{"SnubDodecadodecahedralGraph",{0,Missing["NotAvailable",nicelcf]}}
}

PropertyReplace[l2,"LCFNotations"]

RenameGraphFiles[]

Length[BilateralOrder1LCF=Get[FileNameJoin[{"/","Volumes","eww","mma","Graphs","Properties","LCFNotations-Nice",GraphNameToFileName["SnubDodecadodecahedralGraph","_bilateral-order-1-reserve.log"]}]]]

BilateralLCFGraph@@@BilateralOrder1LCF//Length//Timing

BilateralLCFGraph@@@Take[BilateralOrder1LCF,10]

Length[bilat=SelectBilateralLCFs[BilateralOrder1LCF,"ProgressEvery"->500,Debug->True]]//Timing

LCF compute all

Length[FindHamiltonianCycle[GraphData["SnubDodecadodecahedralGraph"],All][[All,All,1]]]//Timing

Tally[(lcf=LCF[GraphData["SnubDodecadodecahedralGraph"],All])[[All,2]]]//Timing

MaxMemoryUsed[]/10.^9 "GB"

Tally[(lcf=ReadProperty["LCFNotations",GraphNameToFileName["SnubDodecadodecahedralGraph",".m.gz"]])[[All,2]]]//Timing

DeleteCases[lcf,{_,1}]

LCFGraph@@@DeleteCases[lcf,{_,1}]//StyleGraphs

(gs=Flatten[{
(* all LCF's with order >1, sorted by order and with bilateral graphs first *)
Join[DeleteCases[#,{_Missing,_}][[All,1]],Cases[#,{_Missing,_}][[All,2]]]&/@Map[{BilateralLCFGraph@#,#}&,Map[LCFGraph@@#&,SplitBy[DeleteCases[lcf,{_,1}],Last],{2}],{2}],
(* order-1 bilateral only *)
DeleteMissing[BilateralLCFGraph@@@Cases[lcf,{_,1}]]}])//Timing

Length[gs]

UnitDistance

GraphData["SnubDodecadodecahedralGraph","UnitDistance"]

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

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

Select[%,!FreeQ[GraphEmbedding[#],_?InexactNumberQ]&]

UnitDistance by refinement

UnitDistanceEmbeddingRefine[Graph[GraphData["SnubDodecadodecahedralGraph","VertexList"],GraphData["SnubDodecadodecahedralGraph","EdgeList"]],MaxIterations->500]

UnitDistanceGraphEmbeddingQ[%]

UnitDistanceEmbeddingRefine[Annotate[#,VertexCoordinates->N[GraphEmbedding[#]]],MaxIterations->500]&/@Complement@@(GraphData["SnubDodecadodecahedralGraph","Graph",#]&/@{"All","UnitDistance"})

Select[%,UnitDistanceGraphEmbeddingQ]

UnitDistance by FindUnitDistanceEmbedding

FindUnitDistanceEmbedding[GraphData["SnubDodecadodecahedralGraph"],MaxIterations->5000,"ReturnWithMessage"->True]//Timing

FindUnitDistanceEmbedding[GraphData["SnubDodecadodecahedralGraph"],MaxIterations->5000,"ReturnWithMessage"->False]//Quiet//Timing

UnitDistance by FindSubgraphUnitDistanceEmbedding

l={"SnubDodecadodecahedralGraph",FindSubgraphUnitDistanceEmbedding[GraphData["SnubDodecadodecahedralGraph"],TimeConstraint->300,"Results"->All]//Timing}

gs=SortBy[UniqueEmbeddings[l],Replace[RectilinearCrossingCount[#],Infinity->0]&]

Matchstick

GraphData["SnubDodecadodecahedralGraph","Matchstick"]

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

3D default

Graph3D[GraphData["SnubDodecadodecahedralGraph","Edges"]]

3D All

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

3D UnitDistance construction from uniform polyhedron

emb=GraphData["SnubDodecadodecahedralGraph","PolyhedralEmbeddings"]

PolyhedronGraph[PolyhedronData[#,"Polyhedron"]]&/@emb

3D UnitDistance

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

3D Polyhedron

GraphData["SnubDodecadodecahedralGraph","Polyhedral"]

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

GraphData

file=OpenAppend["~/polygraphs.m"]

g=PolyhedronGraph[PolyhedronData["SnubDodecadodecahedron","Polyhedron"]]

lowercasedecamel[s_]:=StringTrim[StringReplace[s,RegularExpression["([A-Z])"]:>" "<>ToLowerCase["$1"]]]

PolyhedronNameToGraphName[s_]:=StringReplace[s,"dron"->"dralGraph"]

With[
{
stdname="SnubDodecadodecahedron",
altnames={"InvertedSnubDodecadodecahedron"}
},
WriteString[file,GraphDataString[g,
"StandardName"->PolyhedronNameToGraphName@stdname,
"AlternateStandatdNames"->PolyhedronNameToGraphName/@altnames,
"Name"->lowercasedecamel@stdname,
"AlternateNames"->lowercasedecamel/@PolyhedronNameToGraphName/@altnames,
"Information"->stdname,
"Classes"->{"UniformSkeleton"},
"Skip"->{"ConnectedInducedSubgraphPolynomial","ConnectedInducedSubgraphs","TuttePolynomial"},
TimeConstraint->10
]]]

Close [file]