# Decagonal-truncated tetrahedral duoprism

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Decagonal-truncated tetrahedral duoprism | |
---|---|

Rank | 5 |

Type | Uniform |

Notation | |

Bowers style acronym | Datut |

Coxeter diagram | x10o x3x3o () |

Elements | |

Tera | 4 triangular-decagonal duoprisms, 10 truncated tetrahedral prisms, 4 hexagonal-decagonal duoprisms |

Cells | 40 triangular prisms, 40 hexagonal prisms, 10 truncated tetrahedra, 6+12 decagonal prisms |

Faces | 40 triangles, 60+120 squares, 40 hexagons, 12 decagons |

Edges | 60+120+120 |

Vertices | 120 |

Vertex figure | Digonal disphenoidal pyramid, edge lengths 1, √3, √3 (base triangle), √(5+√5)/2 (top), √2 (side edges) |

Measures (edge length 1) | |

Circumradius | |

Hypervolume | |

Diteral angles | Tuttip–tut–tuttip: 144° |

Tradedip-dip-hadedip: | |

Tradedip–trip–tuttip: 90° | |

Hadedip-hip-tuttip: 90° | |

Hadedip–dip–hadedip: | |

Central density | 1 |

Number of external pieces | 18 |

Level of complexity | 30 |

Related polytopes | |

Army | Datut |

Regiment | Datut |

Dual | Decagonal-triakis tetrahedral duotegum |

Conjugate | Decagrammic-truncated tetrahedral duoprism |

Abstract & topological properties | |

Euler characteristic | 2 |

Orientable | Yes |

Properties | |

Symmetry | A_{3}×I2(10), order 480 |

Convex | Yes |

Nature | Tame |

The **decagonal-truncated tetrahedral duoprism** or **datut** is a convex uniform duoprism that consists of 10 truncated tetrahedral prisms, 4 hexagonal-decagonal duoprisms, and 4 triangular-decagonal duoprisms. Each vertex joins 2 truncated tetrahedral prisms, 1 triangular-decagonal duoprism, and 2 hexagonal-decagonal duoprisms.

## Vertex coordinates[edit | edit source]

The vertices of a decagonal-truncated tetrahedral duoprism of edge length 1 are given by all permutations and even sign changes of the last three coordinates of:

## Representations[edit | edit source]

A decagonal-truncated tetrahedral duoprism has the following Coxeter diagrams:

- x10o x3x3o (full symmetry)
- x5x x3x3o (decagons as dipentagons)