# Great rhombihexacron

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Great rhombihexacron | |
---|---|

Rank | 3 |

Type | Uniform dual |

Elements | |

Faces | 24 butterflies |

Edges | 24+24 |

Vertices | 12+6 |

Vertex figures | 12 squares |

6 octagrams | |

Measures (edge length 1) | |

Inradius | |

Dihedral angle | |

Central density | odd |

Number of external pieces | 48 |

Related polytopes | |

Dual | Great rhombihexahedron |

Conjugate | Small rhombihexacron |

Convex core | Triakis octahedron |

Abstract & topological properties | |

Flag count | 192 |

Euler characteristic | –6 |

Orientable | No |

Genus | 8 |

Properties | |

Symmetry | B_{3}, order 48 |

Convex | No |

Nature | Tame |

The **great rhombihexacron** is a uniform dual polyhedron. It consists of 24 butterflies.

If its dual, the great rhombihexahedron, has an edge length of 1, then the short edges of the butterflies will measure , and the long edges will be . The butterflies have two interior angles of , and two of . The intersection has an angle of .

## Vertex coordinates[edit | edit source]

A great rhombihexacron with dual edge length 1 has vertex coordinates given by all permutations of:

- ,
- .

## External links[edit | edit source]

- Wikipedia contributors. "Great rhombihexacron".
- McCooey, David. "Great Rhombihexacron"