Archimedean Dual Graph
ArchimedeanDualGraphs
The 13 Archimedean dual graphs are the skeletons of the Archimedean dual solids, illustrated above. Since they are polyhedral graphs, they are also planar. However, none of them are regular.
The following table summarizes properties of the Archimedean dual graphs.
graph G V E |Aut(G)| Hamiltonian Eulerian vertex-transitive edge-transitive
deltoidal
hexecontahedral graph 62 120 120 no no no no
deltoidal
icositetrahedral graph 26 48 48 no no no no
disdyakis
dodecahedral graph 26 72 48 yes yes no no
disdyakis
triacontahedral graph 62 180 120 yes yes no no
pentagonal
hexecontahedral graph 92 150 60 yes no no no
pentagonal
icositetrahedral graph 38 60 24 yes no no no
pentakis
dodecahedral graph 32 90 120 yes no no no
rhombic
dodecahedral graph 14 24 48 no no no yes
rhombic
triacontahedral graph 32 60 120 no no no yes
small
triakis octahedral graph 14 36 48 no no no no
tetrakis
hexahedral graph 14 36 48 yes yes no no
triakis icosahedral
graph 32 90 120 no no no no
triakis tetrahedral
graph 8 18 24 yes no no no
See also
Archimedean Dual, Archimedean GraphExplore with Wolfram|Alpha
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References
House of Graphs. Archimedean Dual Graphs. Deltoidal Hexecontahedral Graph, Deltoidal Icositetrahedral Graph, Disdyakis Dodecahedral Graph, Disdyakis Triacontahedral Graph, Pentagonal Hexecontahedral Graph, Pentagonal Icositetrahedral Graph, Pentakis Dodecahedral Graph, Rhombic Dodecahedral Graph, Rhombic Triacontahedral Graph, Small Triakis Octahedral Graph, Tetrakis Hexahedral Graph, Triakis Icosahedral Graph, and Triakis Tetrahedral Graph.Referenced on Wolfram|Alpha
Archimedean Dual GraphCite this as:
Weisstein, Eric W. "Archimedean Dual Graph." From MathWorld--A Wolfram Resource. https://mathworld.wolfram.com/ArchimedeanDualGraph.html