# Compound of five truncated tetrahedra

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Compound of five truncated tetrahedra | |
---|---|

Rank | 3 |

Type | Uniform |

Notation | |

Bowers style acronym | Taki |

Elements | |

Components | 5 truncated tetrahedra |

Faces | 20 triangles, 20 hexagons |

Edges | 30+60 |

Vertices | 60 |

Vertex figure | Isosceles triangle, edge lengths 1, √3, √3 |

Measures (edge length 1) | |

Circumradius | |

Volume | |

Dihedral angles | 3–6: |

6–6: | |

Central density | 5 |

Number of external pieces | 140 |

Level of complexity | 26 |

Related polytopes | |

Army | Non-uniform Snid, edge lengths (equilateral triangles), (remaining edges) |

Regiment | Taki |

Dual | Compound of five triakis tetrahedra |

Conjugate | Compound of five truncated tetrahedra |

Convex core | Icosahedron |

Abstract & topological properties | |

Flag count | 360 |

Orientable | Yes |

Properties | |

Symmetry | H_{3}+, order 60 |

Convex | No |

Nature | Tame |

The **truncated chiricosahedron**, **taki**, or **compound of five truncated tetrahedra** is a uniform polyhedron compound. It consists of 20 triangles and 20 hexagons, with one triangle and two hexagons joining at each vertex. As the name suggests, it can be derived as the truncation of the chiricosahedron, the compound of five tetrahedra.

Its quotient prismatic equivalent is the truncated tetrahedral pentachoroorthowedge, which is seven-dimensional.

## Gallery[edit | edit source]

## Vertex coordinates[edit | edit source]

The vertices of a truncated chiricosahedron of edge length 1 can be given by all even permutations and all even sign changes of:

## Related polyhedra[edit | edit source]

The truncated icosicosahedron is a compound of the two opposite chiral forms of the truncated chiricosahedron.

## External links[edit | edit source]

- Bowers, Jonathan. "Polyhedron Category C2: Compound Truncates" (#8).

- Klitzing, Richard. "taki".
- Wikipedia contributors. "Compound of five truncated tetrahedra".