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.[1]

Along with the 13, the set of infinite prism graphs and antiprism graphs can also be considered Archimedean graphs.[2]

Name | Graph | Degree | Edges | Vertices | Order |
---|---|---|---|---|---|

truncated tetrahedral graph | 3 | 18 | 12 | 24 | |

cuboctahedral graph | 4 | 24 | 12 | 48 | |

truncated cubical graph | 3 | 36 | 24 | 48 | |

truncated octahedral graph | 3 | 36 | 24 | 48 | |

rhombicuboctahedral graph | 4 | 48 | 24 | 48 | |

truncated cuboctahedral graph (great rhombicuboctahedron) |
3 | 72 | 48 | 48 | |

snub cubical graph | 5 | 60 | 24 | 24 | |

icosidodecahedral graph | 4 | 60 | 30 | 120 | |

truncated dodecahedral graph | 3 | 90 | 60 | 120 | |

truncated icosahedral graph | 3 | 90 | 60 | 120 | |

rhombicosidodecahedral graph | 4 | 120 | 60 | 120 | |

truncated icosidodecahedral graph (great rhombicosidodecahedron) |
3 | 180 | 120 | 120 | |

snub dodecahedral graph | 5 | 150 | 60 | 60 |

See also

Platonic graph

Wheel graph

References

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.

Undergraduate Texts in Mathematics

Graduate Studies in Mathematics

Hellenica World - Scientific Library

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