# Pentagonal duotruncatoprism

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Pentagonal duotruncatoprism | |
---|---|

Rank | 4 |

Type | Isogonal |

Notation | |

Bowers style acronym | Pedtep |

Elements | |

Cells | 25 tetragonal disphenoids, 50 wedges, 25 rectangular trapezoprisms, 10 dipentagonal prisms |

Faces | 100 isosceles triangles, 100 isosceles trapezoids, 50+50 rectangles, 10 dipentagons |

Edges | 50+50+100+100 |

Vertices | 100 |

Vertex figure | Mirror-symmetric bi-apiculated tetrahedron |

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

Edge lengths | Edges of decagons (50+50): 1 |

Lacing edges (100): | |

Edges of pseudo-pentagons (100): | |

Circumradius | |

Central density | 1 |

Related polytopes | |

Army | Pedtep |

Regiment | Pedtep |

Dual | Pentagonal duotruncatotegum |

Abstract & topological properties | |

Euler characteristic | 0 |

Orientable | Yes |

Properties | |

Symmetry | H_{2}≀S_{2}, order 200 |

Convex | Yes |

Nature | Tame |

The **pentagonal duotruncatoprism** or **pedtep** is a convex isogonal polychoron and the fourth member of the duoexpandoprism family. It consists of 10 dipentagonal prisms, 25 rectangular trapezoprisms, 50 wedges, and 25 tetragonal disphenoids. 2 dipentagonal 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 pentagonal-dipentagonal duoprisms whose dipentagonal prism cells have a smaller coircumradius than the pentagonal prisms. However, it cannot be made uniform.