# Compound of ten truncated tetrahedra

The **truncated icosicosahedron**, **te**, or **compound of ten truncated tetrahedra** is a uniform polyhedron compound. It consists of 40 triangles (which form coplanar pairs combining into 20 hexagrams) and 40 hexagons, with one triangle and two hexagons joining at each vertex. As the name suggests, it can be derived as the truncation of the icosicosahedron, the compound of ten tetrahedra. It can alternatively be constructed as the compound of the two chiral forms of the truncated chiricosahedron.

Compound of ten truncated tetrahedra | |
---|---|

Rank | 3 |

Type | Uniform |

Notation | |

Bowers style acronym | Te |

Elements | |

Components | 10 truncated tetrahedra |

Faces | 40 triangles as 20 hexagrams, 40 hexagons as 20 stellated dodecagons |

Edges | 60+120 |

Vertices | 120 |

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

Measures (edge length 1) | |

Circumradius | |

Volume | |

Dihedral angles | 3–6: |

6–6: | |

Central density | 10 |

Number of external pieces | 380 |

Level of complexity | 26 |

Related polytopes | |

Army | Semi-uniform Grid, edge lengths (decagons), (ditrigon-rectangle) |

Regiment | Te |

Dual | Compound of ten triakis tetrahedra |

Conjugate | Compound of ten truncated tetrahedra |

Convex core | Icosahedron |

Abstract & topological properties | |

Flag count | 720 |

Orientable | Yes |

Properties | |

Symmetry | H_{3}, order 120 |

Convex | No |

Nature | Tame |

Its quotient prismatic equivalent is the truncated tetrahedral decayottoorthowedge, which is twelve-dimensional.

## Gallery edit

## Vertex coordinates edit

The vertices of a truncated icosicosahedron of edge length 1 can be given by all even permutations of:

## External links edit

- Bowers, Jonathan. "Polyhedron Category C2: Compound Truncates" (#9).

- Klitzing, Richard. "te".
- Wikipedia contributors. "Compound of ten truncated tetrahedra".