# Decagonal duotruncatoprism

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Decagonal duotruncatoprism | |
---|---|

Rank | 4 |

Type | Isogonal |

Notation | |

Bowers style acronym | Dedtep |

Elements | |

Cells | 100 tetragonal disphenoids, 200 wedges, 100 rectangular trapezoprisms, 20 didecagonal prisms |

Faces | 400 isosceles triangles, 400 isosceles trapezoids, 200+200 rectangles, 20 didecagons |

Edges | 200+200+400+400 |

Vertices | 400 |

Vertex figure | Mirror-symmetric bi-apiculated tetrahedron |

Measures (based on icosagon edge length 1 and same radius ratio as uniform-derived decagonal duoexpandoprism) | |

Edge lengths | Edges of icosagons (200+200): 1 |

Edges of pseudo-decagons (400): | |

Lacing edges (400): | |

Circumradius | |

Central density | 1 |

Related polytopes | |

Army | Dedtep |

Regiment | Dedtep |

Dual | Decagonal duotruncatotegum |

Abstract & topological properties | |

Euler characteristic | 0 |

Orientable | Yes |

Properties | |

Symmetry | I_{2}(10)≀S_{2}, order 800 |

Convex | Yes |

Nature | Tame |

The **decagonal duotruncatoprism** or **dedtep** is a convex isogonal polychoron and the ninth member of the duotruncatoprism family. It consists of 20 didecagonal prisms, 100 rectangular trapezoprisms, 200 wedges, and 100 tetragonal disphenoids. 2 didecagonal 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 decagonal-didecagonal duoprisms whose didecagonal prisms have a smaller circumradius than their decagonal prisms. However, it cannot be made uniform.