# Triangular duotruncatoprism

Jump to navigation
Jump to search

Triangular duotruncatoprism | |
---|---|

Rank | 4 |

Type | Isogonal |

Notation | |

Bowers style acronym | Tridtep |

Elements | |

Cells | 9 tetragonal disphenoids, 18 wedges, 9 rectangular trapezoprisms, 6 ditrigonal prisms |

Faces | 36 isosceles triangles, 36 isosceles trapezoids, 18+18 rectangles, 6 ditrigons |

Edges | 18+18+36+36 |

Vertices | 36 |

Vertex figure | Mirror-symmetric bi-apiculated tetrahedron |

Measures (based on hexagons of edge length 1, triangle radius 2) | |

Edge lengths | Edges of hexagons (18+18): 1 |

Lacing edges (36): | |

Edges of pseudo-triangles (36): | |

Circumradius | |

Central density | 1 |

Related polytopes | |

Army | Tridtep |

Regiment | Tridtep |

Dual | Triangular duotruncatotegum |

Abstract & topological properties | |

Euler characteristic | 0 |

Orientable | Yes |

Properties | |

Symmetry | A_{2}≀S_{2}, order 72 |

Convex | Yes |

Nature | Tame |

The **triangular duotruncatoprism** or **tridtep** is a convex isogonal polychoron and the second member of the duotruncatoprism family. It consists of 6 ditrigonal prisms, 9 rectangular trapezoprisms, 18 wedges, and 9 tetragonal disphenoids. 2 ditrigonal prisms, 2 rectangular trapezoprisms, 3 wedges, and 1 tetragonal disphenoid join at each vertex. It can be obtained as the convex hull of two orthogonal semi-uniform triangular-ditrigonal duoprisms whose ditrigonal prism cells have a smaller circumradius than their triangular prisms. However, it cannot be made uniform.