Bidiakis Cube

Author

Eric W. Weisstein
May 29, 2007

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

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

©2007 Wolfram Research, Inc. except for portions noted otherwise

Canonical Name

GraphData["BidiakisCube","StandardName"]

Embeddings

GraphicsGrid[Partition[GraphData["BidiakisCube","AllImages"],3,3,{1,1},{}]]

LCF

"LCF"/.GraphData["BidiakisCube","NotationRules"]

GraphData

GraphClassString["BidiakisCube"]

Construction

ShowLabeledGraph[g=Graph["CubicalGraph"]]

With[{d=.4},(g2=DeleteEdges[ChangeVertices[g,{{0,1},{0,0},{-d,1+d},{-d,d},{1,1},{1,0},{-d+1,1+d},{-d+1,d}}],{{2,6},{4,8},{1,3},{5,7}}])
]//ShowLabeledGraph

v=Vertices[g2];
(g3=AddEdges[AddVertices[g2,Mean[v[[#]]]&/@{{1,3},{5,7},{2,6},{4,8}}],{{1,9},{3,9},{5,10},{7,10},{4,12},{8,12},{2,11},{6,11},{11,12},{9,10}}])//ShowLabeledGraph

(g4=ChangeVertices[g3,{{1/3,1/3},{0,0},{1/3,2/3},{0,1},{2/3,1/3},{1,0},{2/3,2/3},{1,1},{1/3,1/2},{2/3,1/2},{1/2,0},{1/2,1}}])//ShowGraph

RecognizeGraph[g3]

ToCommonEdges[#,Graph[{"CubicPolyhedral",4}]]&/@{g3,g4}