Archimedean Dual Graph


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 GVE|Aut(G)|HamiltonianEulerianvertex-transitiveedge-transitive
deltoidal hexecontahedral graph62120120nononono
deltoidal icositetrahedral graph264848nononono
disdyakis dodecahedral graph267248yesyesnono
disdyakis triacontahedral graph62180120yesyesnono
pentagonal hexecontahedral graph9215060yesnonono
pentagonal icositetrahedral graph386024yesnonono
pentakis dodecahedral graph3290120yesnonono
rhombic dodecahedral graph142448nononoyes
rhombic triacontahedral graph3260120nononoyes
small triakis octahedral graph143648nononono
tetrakis hexahedral graph143648yesyesnono
triakis icosahedral graph3290120nononono
triakis tetrahedral graph81824yesnonono

See also

Archimedean Dual, Archimedean Graph

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Cite this as:

Weisstein, Eric W. "Archimedean Dual Graph." From MathWorld--A Wolfram Web Resource.

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