# Decagonal-tetrahedral duoprism

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

Rank | 5 |

Type | Uniform |

Notation | |

Bowers style acronym | Datet |

Coxeter diagram | x10o x3o3o () |

Elements | |

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

Cells | 10 tetrahedra, 40 triangular prisms6 decagonal prisms |

Faces | 40 triangles, 60 squares, 4 decagons |

Edges | 40+60 |

Vertices | 40 |

Vertex figure | Triangular scalene, edge lengths 1 (base triangle), √(5+√5)/2 (top), √2 (sides) |

Measures (edge length 1) | |

Circumradius | |

Hypervolume | |

Diteral angles | Tepe–tet–tepe: 144° |

Tepe–trip–tradedip: 90° | |

Tradedip–dip–tradedip: | |

Heights | Dec atop tradedip: |

Dip atop perp dip: | |

Central density | 1 |

Number of external pieces | 14 |

Level of complexity | 10 |

Related polytopes | |

Army | Datet |

Regiment | Datet |

Dual | Decagonal-tetrahedral duotegum |

Conjugate | Decagrammic-tetrahedral duoprism |

Abstract & topological properties | |

Euler characteristic | 2 |

Orientable | Yes |

Properties | |

Symmetry | A_{3}×I2(10), order 480 |

Convex | Yes |

Nature | Tame |

The **decagonal-tetrahedral duoprism** or **datet** is a convex uniform duoprism that consists of 10 tetrahedral prisms and 4 triangular-decagonal duoprisms. Each vertex joins 2 tetrahedral prisms and 3 triangular-decagonal duoprisms.

## Vertex coordinates[edit | edit source]

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

## Representations[edit | edit source]

A decagonal-tetrahedral duoprism has the following Coxeter diagrams:

- x10o x3o3o (full symmetry)
- x5x x3o3o (decagons as dipentagons)