# Pentagonal antitegum

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Pentagonal antitegum | |
---|---|

Rank | 3 |

Type | Uniform dual |

Space | Spherical |

Notation | |

Bowers style acronym | Pat |

Coxeter diagram | p2p10o () |

Elements | |

Faces | 10 kites |

Edges | 10+10 |

Vertices | 2+10 |

Vertex figure | 2 pentagons, 10 triangles |

Measures (edge length 1) | |

Dihedral angle | |

Central density | 1 |

Related polytopes | |

Army | Pat |

Regiment | Pat |

Dual | Pentagonal antiprism |

Conjugate | Pentagrammic retroantitegum |

Abstract & topological properties | |

Euler characteristic | 2 |

Surface | Sphere |

Orientable | Yes |

Genus | 0 |

Properties | |

Symmetry | I_{2}(10)×A_{1}/2, order 20 |

Convex | Yes |

Nature | Tame |

The **pentagonal antitegum** or **pat**, also known as the **pentagonal trapezohedron**, is an antitegum based on the pentagon, constructed as the dual of a pentagonal antiprism. It has 10 kites as faces, with 2 order–5 and 10 order–3 vertices.

Each face of this polyhedron is a kite with its longer edges times the length of its shorter edges. These kites have 3 angles measuring 108° and 1 measuring 36°.

The pentagonal antitegum can be constructed from the regular dodecahedron by augmenting tall pyramids on two opposite faces.

## External links[edit | edit source]

- Klitzing, Richard. "p2p5p".

- Wikipedia Contributors. "Pentagonal trapezohedron".
- McCooey, David. "Pentagonal Trapezohedron"