# Great hexacronic icositetrahedron

Great hexacronic icositetrahedron | |
---|---|

Rank | 3 |

Type | Uniform dual |

Notation | |

Coxeter diagram | m4/3m3o4*a |

Elements | |

Faces | 24 kites |

Edges | 24+24 |

Vertices | 6+6+8 |

Vertex figures | 8 triangles |

6 squares | |

6 octagrams | |

Measures (edge length 1) | |

Inradius | |

Dihedral angle | |

Central density | 4 |

Number of external pieces | 48 |

Related polytopes | |

Dual | Great cubicuboctahedron |

Conjugate | Small hexacronic icositetrahedron |

Convex core | Triakis octahedron |

Abstract & topological properties | |

Flag count | 192 |

Euler characteristic | –4 |

Orientable | Yes |

Genus | 3 |

Properties | |

Symmetry | B_{3}, order 48 |

Convex | No |

Nature | Tame |

The **great hexacronic icositetrahedron** is a uniform dual polyhedron. It consists of 24 kites.

If its dual, the great cubicuboctahedron, has an edge length of 1, then the short edges of the kites will measure , and the long edges will be . The kite faces will have length , and width . The kites have two interior angles of , one of , and one of .

## Vertex coordinates[edit | edit source]

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

## External links[edit | edit source]

- Wikipedia contributors. "Great hexacronic icositetrahedron".
- McCooey, David. "Great Hexacronic Icositetrahedron"