Superbox Graph

Author

Eric W. Weisstein
July 26, 2026

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

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

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

Figure

Quit

GraphicsGrid[
Partition[
StyleGraphs[
GraphData["SuperboxGraph","Graph","All"]
],
UpTo[4]
],
Dividers->All
]

Embeddings

<<MathWorld`Graphs`

Names

GraphData["SuperboxGraph","StandardName"]

GraphData["SuperboxGraph","StandardNames"]

HouseOfGraphs

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

HouseOfGraphsLookup[hogid]

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

Wikidata

GraphData["SuperboxGraph","WikidataID"]

GraphData["SuperboxGraph","WikidataID","URL"]

Robertson et al. 2019 construction

v=Join[Table[{i,2},{i,0,4}],Table[{i,0},{i,0,4}],{{0,1},{1/2,1},{1,1},{3,1},{7/2,1},{4,1}}];
g=Graph[Range[Length[v]],UndirectedEdge@@@Sort[{{6,7},{7,8},{8,9},{9,10},{1,2},{2,3},{3,4},{4,5},{3,8},{6,11},{1,11},{2,13},{7,13},{4,14},{9,14},{10,16},{5,16},{11,12},{12,13},{14,15},{15,16},{1,5},{6,10},{12,15}}],VertexCoordinates->v,VertexLabels->"Name"]

CubicGraphQ[g]

r=RecognizeGraph[g]

PlanarGraphQ[g]

AlmostPlanarGraphQ[g]

CrossingNumber[g,TimeConstraint->10]

Primary

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

All

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

CurvedEdge

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

Inexact

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

Degenerate

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

DegenerateGraphEmbeddingTypes/@GraphData["SuperboxGraph","Graph","Degenerate"]//Column

Embeddings

GraphDataEmbeddings[GraphData["SuperboxGraph"]]

Default embedding

g0=GraphPlot[Graph[GraphData["SuperboxGraph","VertexList"],GraphData["SuperboxGraph","Edges"]]]

Configuration

GraphData["SuperboxGraph","Configuration"]

configurations=GraphData["SuperboxGraph","Graph","Configuration"]//StyleGraphs

GeneralizedPetersen

GraphData["SuperboxGraph","Graph","GeneralizedPetersen"]//StyleGraphs

IGraph

GraphData["SuperboxGraph","Graph","IGraph"]//StyleGraphs

CompleteKPartite

GraphData["SuperboxGraph","Graph","CompleteKPartite"]//StyleGraphs

Bipartite

GraphData["SuperboxGraph","Bipartite"]

GraphData["SuperboxGraph","Graph","Bipartite"]//StyleGraphs

Bilateral

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

Grid[DeleteCases[Monitor[{g=#,BilateralGraphEmbeddingTypes[#],GraphSymmetryGroup[#]}&/@GraphData["SuperboxGraph","Graph","All"],g],{_,_,TransformationGroup[{}]}],Dividers->All,Alignment->{{Center,{Left}}}]//Quiet

Circular

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

Circular construction All

GraphData["SuperboxGraph","Hamiltonian"]

GraphData["SuperboxGraph","HamiltonianCycles"]

GraphData["SuperboxGraph","HamiltonianCycleCount"]

GraphData["SuperboxGraph","LCF"]

GraphData["SuperboxGraph","LCFSignature"]

BilateralHamiltonianCycleQ[GraphData["SuperboxGraph"]]

FindBilateralHamiltonianCycle[GraphData["SuperboxGraph"]]

Planar

GraphData["SuperboxGraph","Planar"]

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

MinimalCrossing

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

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

MinimalCrossing construction

CrossingNumber[GraphData["SuperboxGraph"],TimeConstraint->10]//AbsoluteTiming

CrossingNumber[GraphData["SuperboxGraph"],TimeConstraint->60]//AbsoluteTiming

g=RotateGraph[MinimalCrossingGraph[GraphData["SuperboxGraph"],"CrossingNumber"->2]]

RecognizeGraph[g]

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

RecognizeGraph[g]

RectilinearCrossingCount[g]

MinimalRectiinearCrossing 1

mc=MinimalCrossingGraph[GraphData["SuperboxGraph"],"CrossingNumber"->2]

mc2=VertexDelete[mc,{17,18}]

d=VertexDegree[mc2]

UndirectedEdge@@@{{6,7},{9,10},{12,15}}

sub=Select[Subsets[Subsets[Position[d,2]//Flatten,{2}],{3}],Length[Union@Flatten[#]]==6&&Intersection[#,List@@@EdgeList[mc2]]==={}&]

gs=SetProperty[EdgeAdd[mc2,UndirectedEdge@@@#],{VertexLabels->None,VertexCoordinates->Take[GraphEmbedding[mc],16]}]&/@sub

Select[gs,IsomorphicGraphQ[#,GraphData["SuperboxGraph"]]&]

GraphPlot[%[[1]]]

Rotate[,-.5]

v=Join[CirclePoints[6],Table[v[[5]]+(v[[2]]-v[[5]])i/3,{i,2}],Table[v[[7]]+{0,(v[[4,2]]-v[[7,2]])/3}+i(v[[8]]-v[[7]])/4,{i,0,4}],
Table[v[[7]]+{0,(v[[4,2]]-v[[7,2]])2/3}+i(v[[8]]-v[[7]])/2,{i,0,2}]];
g=Graph[Range[Length[v]],UndirectedEdge@@@Sort[Sort/@{{1,6},{1,2},{2,3},{3,4},{4,5},{5,7},{7,8},{2,8},{5,6},{6,10},{1,12},{7,9},{9,14},{14,15},{15,16},{13,16},{8,13},{11,15},{9,10},{10,11},{11,12},{12,13},{4,14},{3,16}}],VertexLabels->"Name",VertexCoordinates->v]

r=RecognizeGraph[g]

rcn=RectilinearCrossingCount@g

vs=ToCommonEdges[g,GraphData[r]]

MinimalRectiinearCrossing 2

GraphPlot@SetProperty[,VertexLabels->None]

v={{0,0},{1,0},{1,3/8},{1,1},{0,1},{0,3/8},{1/6,3/8},{5/6,3/8},{1/6,1/2},{2/6,1/2},{3/6,1/2},{4/6,1/2},{5/6,1/2},{1/6,3/4},{3/6,3/4},{5/6,3/4}};
g=Graph[Range[Length[v]],UndirectedEdge@@@Sort[Sort/@{Sequence@@Partition[Range[6],2,1,1],{1,10},{2,12},{5,14},{4,16},{14,15},{15,16},{9,10},{10,11},{11,12},{12,13},{6,7},{7,8},{3,8},{8,13},{13,16},{7,9},{9,14},{11,15}}],VertexLabels->"Name",VertexCoordinates->v]

r=RecognizeGraph[g]

rcn=RectilinearCrossingCount@g

vs=ToCommonEdges[g,GraphData[r]]

Circulant

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

Circulant construction

GraphData["SuperboxGraph","NotationRules","Circulant"]

(ci=CirculantIndices[GraphData["SuperboxGraph"]])//AbsoluteTiming

CirculantGraph1@@@ci

Cases[GraphData["SuperboxGraph","StandardNames"],{"Circulant",i_}:>i]

CirculantGraph1@@@%

Complement graph

compl=GraphData["SuperboxGraph","ComplementGraph","Name"]

Line graph

GraphData["SuperboxGraph","Line"]

LineGraphQ[GraphData["SuperboxGraph"]]//Timing

RootGraph

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

RootGraph[GraphData["SuperboxGraph"]]

Halin

GraphData["SuperboxGraph","Halin"]

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

Rigid

GraphData["SuperboxGraph","Rigid"]

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

Flexible

GraphData["SuperboxGraph","Flexible"]

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

Voltage

gs=GraphData["SuperboxGraph","Graph","Voltage"]//StyleGraphs

VoltageGraphNotation/@gs//Column

Voltage construction

VoltageGraph[GraphData["SuperboxGraph"],"MaxResults"->20,Debug->True]

LCF

GraphData["SuperboxGraph","LCF"]

GraphData["SuperboxGraph","HamiltonianCycleCount"]

GraphData["SuperboxGraph","LCFSignature"]

GraphData["SuperboxGraph","LCFNotations"]

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

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

LCF compute All

Divisors[GraphData["SuperboxGraph","V"]]

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

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

MaxMemoryUsed[]/10.^9 "GB"

DeleteCases[lcf,{_,1}]

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

Tally[LCFNotation[#][[-1]]&/@(nicelcfgs=NiceLCFGraphs[lcf,2,1])]//Timing

Length[gs=nicelcfgs]

gs

NiceLCFEmbeddingsWithSymmetryGroups={#,GraphSymmetryGroup[#]}&/@gs;

DeleteCases[NiceLCFEmbeddingsWithSymmetryGroups,{_,TransformationGroup[{Reflection[InfiniteLine[{0,0},{0,-1}]]}]}]

UnitDistance

GraphData["SuperboxGraph","UnitDistance"]

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

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

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

Select[UnitDistanceEmbeddingRefine/@Complement@@(GraphData["SuperboxGraph","Graph",#]&/@{"All","UnitDistance"}),UnitDistanceGraphEmbeddingQ]

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

UnitDistance construction

UnitDistanceEmbeddingRefine[GraphicsToGraph[]]

UnitDistanceGraphEmbeddingQ[%]

(soln=NSolve[{
(*1*)a^2+b^2==1,
(*2*)(a-e)^2+(b-f)^2==1,
(*3*)(c-1/2)^2+(d-u)^2==1,
(*4*)(e-g)^2+(h-f)^2==1,
(*5*)g^2+(h+1)^2==1,
(*6*)(a-1/2)^2+(u-b)^2==1,
(*7*)(e-1/2)^2+(f-z)^2==1,
(*8*)(c-1/2)^2+(d-z)^2==1,
(*9*)(c-1/2)^2+(d-v)^2==1,
(*10*)(g-1/2)^2+(h-v)^2==1,
h==1/2},{h,u,z,v,a,b,c,d,e,f,g},Reals])//Timing

(soln=NSolve[{
(*1*)a^2+b^2==1,
(*2*)(a-e)^2+(b-f)^2==1,
(*3*)(c-1/2)^2+(d-u)^2==1,
(*4*)(e-g)^2+(h-f)^2==1,
(*5*)g^2+(h+1)^2==1,
(*6*)(a-1/2)^2+(u-b)^2==1,
(*7*)(e-1/2)^2+(f-z)^2==1,
(*8*)(c-1/2)^2+(d-z)^2==1,
(*9*)(c-1/2)^2+(d-v)^2==1,
(*10*)(g-1/2)^2+(h-v)^2==1,
h==-1/2},{h,u,z,v,a,b,c,d,e,f,g},Reals])//Timing

soln=NSolve[{
(*1*)a^2+b^2==1,
(*2*)(a-e)^2+(b-f)^2==1,
(*3*)(c-1/2)^2+(d-u)^2==1,
(*4*)(e-g)^2+(h-f)^2==1,
(*5*)g^2+(h+1)^2==1,
(*6*)(a-1/2)^2+(u-b)^2==1,
(*7*)(e-1/2)^2+(f-z)^2==1,
(*8*)(c-1/2)^2+(d-z)^2==1,
(*9*)(c-1/2)^2+(d-v)^2==1,
(*10*)(g-1/2)^2+(h-v)^2==1},{h,u,z,v,a,b,c,d,e,f,g},Reals]

{{h->-0.0019389571201847433`,u->0.8250333141337751`,z->-0.17496668586622488`,v->0.8250333141337751`,a->0.9991389760390071`,b->-0.04148863169260237`,c->1.3660254037844386`,d->0.3250333141337751`,e->0.5`,f->0.8250333141337751`,g->-0.06224270789141144`},{h->-0.5`,u->0.4306048591020996`,z->0.4306048591020996`,v->0.4306048591020996`,a->0.8660254037844386`,b->-0.5`,c->-0.21732656874515044`,d->1.1273419643091562`,e->1.4889401507598758`,f->0.2822897276588305`,g->0.8660254037844386`},{h->-0.5`,u->0.4306048591020996`,z->0.4306048591020996`,v->0.4306048591020996`,a->0.8660254037844386`,b->-0.5`,c->1.2649546972949373`,d->-0.21347922786668358`,e->1.4889401507598758`,f->0.2822897276588305`,g->0.8660254037844386`},{h->-0.6946968003773746`,u->0.19719177934828122`,z->-0.8028082206517188`,v->0.19719177934828122`,a->0.6033855979915972`,b->-0.7974495721588436`,c->1.3660254037844386`,d->-0.30280822065171885`,e->0.5`,f->0.19719177934828122`,g->0.9522551949452349`},{h->-0.5`,u->0.4306048591020996`,z->-1.421756950356318`,v->0.4306048591020996`,a->0.8660254037844386`,b->-0.5`,c->0.8770794766557631`,d->-0.4955760456271092`,e->1.490096382197623`,f->-1.2813676560380594`,g->0.8660254037844386`},{h->-1.6665739922754188`,u->0.7836420561494158`,z->-0.6971619231303884`,v->-0.6971619231303884`,a->0.996428964546977`,b->-0.08443529245427636`,c->-0.17216433536544787`,d->0.04324006650951376`,e->1.4622549149278627`,f->-0.9693116589325232`,g->0.7454388726260591`},{h->-1.7085201845342306`,u->-1.2607318094330986`,z->-1.2607318094330986`,v->-2.687137269445364`,a->-0.43317511933626884`,b->-0.9013097780386105`,c->-0.20095782035140972`,d->-1.9739345394392314`,e->-0.27785616953556913`,f->-1.8891741532606385`,g->0.7056905469875445`},{h->-0.1389638608442633`,u->-0.4537838001359097`,z->-0.4537838001359097`,v->0.8609996404778327`,a->0.8825961866274582`,b->0.4701318659170733`,c->1.2535490203510136`,d->0.20360792017096152`,e->1.4914325310700323`,f->-0.32316398411984915`,g->0.5085437710441283`},{h->-0.5`,u->0.4306048591020996`,z->1.1977756725077149`,v->0.4306048591020996`,a->0.8660254037844386`,b->-0.5`,c->-0.4235054064620529`,d->0.8141902658049073`,e->1.1677541739147193`,f->0.45339380597718815`,g->0.8660254037844386`},{h->-1.2945238614146126`,u->-0.5335512635311613`,z->-0.5335512635311613`,v->-0.40436183645482415`,a->0.9291602966305527`,b->0.3696770795781413`,c->1.4979115807439665`,d->-0.46895654999299274`,e->1.4967988388660596`,f->-0.45360081115423384`,g->0.9556441257379371`},{h->-1.2283172414491732`,u->-0.34757008560095376`,z->-0.9137399218812292`,v->-0.34757008560095376`,a->0.7936817802941565`,b->0.6083331584165853`,c->1.45909484886763`,d->-0.6306550037360914`,e->1.2672685700859243`,f->-0.27241399743163425`,g->0.9735867897917678`},{h->-1.330430734722996`,u->-0.5630137902393052`,z->-0.4343198518061192`,v->-0.4343198518061192`,a->0.9426938202206355`,b->0.33365904950686426`,c->1.4979275863271035`,d->-0.4986668210227122`,e->1.4979699112299607`,f->-0.49800702696457844`,g->0.9438302440324855`},{h->-1.8596960166206329`,u->-1.765434461820091`,z->-1.765434461820091`,v->-2.8596376302105777`,a->-0.1328248913926471`,b->-0.99113952006089`,c->1.3370662199438317`,d->-2.3125360460153344`,e->-0.486971535281584`,f->-1.9263294230336512`,g->0.5108059895954787`},{h->-0.08998380220024046`,u->0.5610469820241998`,z->-0.4944053457573196`,v->-0.4944053457573196`,a->0.9418463777077216`,b->-0.33604374834066436`,c->1.3494145607094001`,d->0.0333208181334401`,e->0.3929529828757251`,f->0.49984861381477846`,g->-0.4145726953648406`},{h->-0.5`,u->0.4306048591020996`,z->-1.5631787453153518`,v->0.4306048591020996`,a->0.8660254037844386`,b->-0.5`,c->0.4212171675487676`,d->-0.5662869431066261`,e->-0.09893826235286288`,f->-0.762383541852111`,g->0.8660254037844386`},{h->-0.7072496520401123`,u->-1.5971326091537779`,z->-0.5971326091537777`,v->-1.5971326091537779`,a->-0.27252529493229005`,b->-0.9621486182612685`,c->-0.36602540378443865`,d->-1.0971326091537779`,e->0.5`,f->-1.5971326091537779`,g->0.9561889111307266`},{h->-0.5`,u->0.4306048591020996`,z->-0.7570823137269191`,v->0.4306048591020996`,a->0.8660254037844386`,b->-0.5`,c->-0.30458050863437724`,d->-0.16323872731240976`,e->1.2432134528281193`,f->-1.4261366938301396`,g->0.8660254037844386`},{h->-1.2537686405225168`,u->-0.3696513012521087`,z->-1.3696513012521088`,v->-0.3696513012521087`,a->0.8150191571099675`,b->0.579434011379862`,c->1.3660254037844386`,d->-0.8696513012521088`,e->0.5`,f->-0.3696513012521087`,g->0.9672649466859397`},{h->-0.4109944761265913`,u->-0.7004493526920142`,z->-0.7004493526920142`,v->0.540350106401296`,a->0.9847053091443915`,b->0.1742281669043453`,c->1.2842857741782885`,d->-0.08004962314535909`,e->-0.015140297517412757`,f->0.15665651817439835`,g->0.8081290075517716`},{h->-0.5459482804199236`,u->0.374452878057158`,z->-0.7897790866356994`,v->0.374452878057158`,a->0.8194503855293622`,b->-0.5731501248850772`,c->-0.3131057637828257`,d->-0.20766310428927073`,e->1.2104257140016919`,f->-1.493551283362159`,g->0.8909753284723296`},{h-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gs=Graph[Range[16],UndirectedEdge@@@{{1,2},{1,3},{1,8},{2,4},{2,7},{3,5},{3,9},{4,5},{4,6},{5,10},{6,13},{6,15},{7,11},{7,13},{8,11},{8,12},{9,12},{9,14},{10,14},{10,16},{11,15},{12,16},{13,14},{15,16}},VertexCoordinates->({{0,0},{-a,b},{a,b},{-1/2,u},{1/2,u},{-c,d},{-e,f},{0,-1},{e,f},{c,d},{-g,h},{g,h},{-1/2,z},{1/2,z},{-1/2,v},{1/2,v}}/.#),VertexLabels->"Name"]&/@soln

RecognizeGraph@gs[[1]]

Select[gs,UnitDistanceGraphEmbeddingQ[#]&&!DegenerateEmbeddingQ[#]&]

MinMax[h/.soln]

Do[
soln=NSolve[{
(*1*)a^2+b^2==1,
(*2*)(a-e)^2+(b-f)^2==1,
(*3*)(c-1/2)^2+(d-u)^2==1,
(*4*)(e-g)^2+(h-f)^2==1,
(*5*)g^2+(h+1)^2==1,
(*6*)(a-1/2)^2+(u-b)^2==1,
(*7*)(e-1/2)^2+(f-z)^2==1,
(*8*)(c-1/2)^2+(d-z)^2==1,
(*9*)(c-1/2)^2+(d-v)^2==1,
(*10*)(g-1/2)^2+(h-v)^2==1},{u,z,v,a,b,c,d,e,f,g},Reals];
gs=Graph[Range[16],UndirectedEdge@@@{{1,2},{1,3},{1,8},{2,4},{2,7},{3,5},{3,9},{4,5},{4,6},{5,10},{6,13},{6,15},{7,11},{7,13},{8,11},{8,12},{9,12},{9,14},{10,14},{10,16},{11,15},{12,16},{13,14},{15,16}},VertexCoordinates->({{0,0},{-a,b},{a,b},{-1/2,u},{1/2,u},{-c,d},{-e,f},{0,-1},{e,f},{c,d},{-g,h},{g,h},{-1/2,z},{1/2,z},{-1/2,v},{1/2,v}}/.#),VertexLabels->"Name"]&/@soln;
Print[h->Select[gs,UnitDistanceGraphEmbeddingQ[#]&&!DegenerateEmbeddingQ[#]&]],
{h,-2,0,.1}];

Timing[1]

Do[
t=(soln=NSolve[{
(*1*)a^2+b^2==1,
(*2*)(a-e)^2+(b-f)^2==1,
(*3*)(c-1/2)^2+(d-u)^2==1,
(*4*)(e-g)^2+(h-f)^2==1,
(*5*)g^2+(h+1)^2==1,
(*6*)(a-1/2)^2+(u-b)^2==1,
(*7*)(e-1/2)^2+(f-z)^2==1,
(*8*)(c-1/2)^2+(d-z)^2==1,
(*9*)(c-1/2)^2+(d-v)^2==1,
(*10*)(g-1/2)^2+(h-v)^2==1},{u,z,v,a,b,c,d,e,f,g},Reals];
gs=(Graph[Range[16],UndirectedEdge@@@{{1,2},{1,3},{1,8},{2,4},{2,7},{3,5},{3,9},{4,5},{4,6},{5,10},{6,13},{6,15},{7,11},{7,13},{8,11},{8,12},{9,12},{9,14},{10,14},{10,16},{11,15},{12,16},{13,14},{15,16}},VertexCoordinates->({{0,0},{-a,b},{a,b},{-1/2,u},{1/2,u},{-c,d},{-e,f},{0,-1},{e,f},{c,d},{-g,h},{g,h},{-1/2,z},{1/2,z},{-1/2,v},{1/2,v}}/.#),VertexLabels->"Name"]&/@soln))//Timing;
Print[{h,t[[1]]}->Select[gs,UnitDistanceGraphEmbeddingQ[#]&&!DegenerateEmbeddingQ[#]&]],
{h,-2,0,.05}];

UnitDistance FindSubgraphUnitDistanceEmbedding

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

gs=UniqueEmbeddings[l]

gs={,,,,,,,,,,,,,,}

Matchstick

GraphData["SuperboxGraph","Matchstick"]

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

3D default

Graph3D[GraphData["SuperboxGraph","Edges"]]

3D All

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

3D UnitDistance

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

3D Polyhedron

GraphData["SuperboxGraph","Polyhedral"]

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

GraphData

GraphDataString

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

WriteString[file,GraphDataString[g,
"StandardName"->"SuperboxGraph",
"Name"->"superbox graph",
TimeConstraint->10,
Debug->True,
"Skip"->{"Arboricity"}
]]

Close[file]