In the mathematical field of graph theory, an Archimedean graph is a graph that forms the skeleton of one of the Archimedean solids. There are 13 Archimedean graphs, and all of them are regular, polyhedral (and therefore by necessity also 3-vertex-connected planar graphs), and also Hamiltonian graphs.
Along with the 13, the set of infinite prism graphs and antiprism graphs can also be considered Archimedean graphs.
|truncated tetrahedral graph||3||18||12||24|
|truncated cubical graph||3||36||24||48|
|truncated octahedral graph||3||36||24||48|
|truncated cuboctahedral graph|
|snub cubical graph||5||60||24||24|
|truncated dodecahedral graph||3||90||60||120|
|truncated icosahedral graph||3||90||60||120|
|truncated icosidodecahedral graph|
|snub dodecahedral graph||5||150||60||60|
- An Atlas of Graphs, p. 267-270
- An Atlas of Graphs, p. 261
- Read, R. C. and Wilson, R. J. An Atlas of Graphs, Oxford, England: Oxford University Press, 2004 reprint, Chapter 6 special graphs pp. 261, 267-269.
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