# Truncated tetracontoctachoron

Truncated tetracontoctachoron | |
---|---|

Rank | 4 |

Type | Isogonal |

Notation | |

Bowers style acronym | Ticont |

Elements | |

Cells | 288 tetragonal disphenoids, 48 ditruncated cubes |

Faces | 1152 isosceles triangles, 192 ditrigons, 144 dioctagons |

Edges | 576+576+1152 |

Vertices | 1152 |

Vertex figure | Sphenoid |

Measures (variant with regular hexagons of edge length 1) | |

Edge lengths | Edges of hexagons (288+288): 1 |

Lacing edges (576): | |

Circumradius | |

Central density | 1 |

Related polytopes | |

Army | Ticont |

Regiment | Ticont |

Dual | Tetrakis bitetracontoctachoron |

Abstract & topological properties | |

Euler characteristic | 0 |

Orientable | Yes |

Properties | |

Symmetry | F_{4}×2, order 2304 |

Convex | Yes |

Nature | Tame |

The **truncated tetracontoctachoron** or **ticont** is a convex isogonal polychoron that consists of 48 ditruncated cubes and 288 tetragonal disphenoids. 1 tetragonal disphenoid and 3 ditruncated cubes join at each vertex. It can be formed by truncating the tetracontoctachoron.

It can also be formed as the convex hull of 2 oppositely oriented semi-uniform variants of the great rhombated icositetrachoron, where if the great rhombated icositetrachora are of the form a3b4c3o, then It is one of five polychora (including two transitional cases) formed from two great rhombated icositetrachora, and is the transitional point between the medial bicantitruncatotetracontoctachoron and great bicantitruncatotetracontoctachoron.

Using the ratio method, the lowest possible ratio between the longest and shortest edges is 1: ≈ 1:1.84776, represented as two variants with either regular hexagons or regular hexadecagons as faces.

## Vertex coordinates[edit | edit source]

The vertices of a truncated tetracontoctachoron with hexagons of edge length 1, centered at the origin, are given by all permutations of:

## External links[edit | edit source]

- Klitzing, Richard. "ticont".