# Enneagonal-tetrahedral duoprism

Jump to navigation
Jump to search

Enneagonal-tetrahedral duoprism | |
---|---|

Rank | 5 |

Type | Uniform |

Notation | |

Bowers style acronym | Etet |

Coxeter diagram | x9o x3o3o () |

Elements | |

Tera | 9 tetrahedral prisms, 4 triangular-enneagonal duoprisms |

Cells | 9 tetrahedra, 36 triangular prisms, 6 enneagonal prisms |

Faces | 36 triangles, 54 squares, 4 enneagons |

Edges | 36+54 |

Vertices | 36 |

Vertex figure | Triangular scalene, edge lengths 1 (base triangle), 2cos(π/9) (top), √2 (sides) |

Measures (edge length 1) | |

Circumradius | |

Hypervolume | |

Diteral angles | Tepe–tet–tepe: 140° |

Tepe–trip–tedip: 90° | |

Tedip–ep–tedip: | |

Heights | En atop tedip: |

Ep atop perp ep: | |

Central density | 1 |

Number of external pieces | 13 |

Level of complexity | 10 |

Related polytopes | |

Army | Etet |

Regiment | Etet |

Dual | Enneagonal-tetrahedral duotegum |

Conjugates | Enneagrammic-tetrahedral duoprism, Great enneagrammic-tetrahedral duoprism |

Abstract & topological properties | |

Euler characteristic | 2 |

Orientable | Yes |

Properties | |

Symmetry | A_{3}×I2(9), order 432 |

Convex | Yes |

Nature | Tame |

The **enneagonal-tetrahedral duoprism** or **etet** is a convex uniform duoprism that consists of 9 tetrahedral prisms and 4 triangular-enneagonal duoprisms. Each vertex joins 2 tetrahedral prisms and 3 triangular-enneagonal duoprisms.

## Vertex coordinates[edit | edit source]

The vertices of an enneagonal-tetrahedral duoprism of edge length 2sin(π/9) are given by all even sign changes of the last three coordinates of:

where j = 2, 4, 8.