The rhombic triacontahedral graph is Archimedean dual graph which is the skeleton of the rhombic
triacontahedron, great rhombic triacontahedron,
and small triambic icosahedron.

It is implemented in the Wolfram Language
as `GraphData`[`"RhombicTriacontahedralGraph"`].

The plots above show the adjacency, incidence, and graph distance matrices for the deltoidal
hexecontahedral graph.

The following table summarizes some properties of the graph.

property | value |

automorphism group order | 120 |

characteristic polynomial | |

chromatic number | 2 |

chromatic
polynomial | ? |

claw-free | no |

clique number | 2 |

determined by spectrum | ? |

diameter | 6 |

distance-regular graph | no |

dual graph name | icosidodecahedral
graph |

edge chromatic number | 5 |

edge connectivity | 3 |

edge count | 60 |

Eulerian | no |

girth | 4 |

Hamiltonian | no |

Hamiltonian cycle count | 0 |

Hamiltonian path count | 0 |

integral graph | no |

independence
number | 20 |

line graph | ? |

perfect matching graph | no |

planar | yes |

polyhedral graph | yes |

polyhedron embedding names | rhombic
triacontahedron |

radius | 6 |

regular | no |

square-free | no |

traceable | no |

triangle-free | yes |

vertex connectivity | 3 |

vertex count | 32 |

## See also

Archimedean Dual Graph,

Rhombic Triacontahedron
## Explore with Wolfram|Alpha

## Cite this as:

Weisstein, Eric W. "Rhombic Triacontahedral
Graph." From *MathWorld*--A Wolfram Web Resource. https://mathworld.wolfram.com/RhombicTriacontahedralGraph.html

## Subject classifications