# Pentagonal duotegum

The **pentagonal duotegum** or **pedit**, also known as the **pentagonal-pentagonal duotegum**, the **5 duotegum**, or the **5-5 duotegum**, is a noble duotegum that consists of 25 tetragonal disphenoids and 10 vertices, with 10 cells joining at each vertex. It is also the 10-4 step prism and the square funk tegum. It is the first in an infinite family of isogonal pentagonal hosohedral swirlchora and also the first in an infinite family of isochoric pentagonal dihedral swirlchora.

Pentagonal duotegum | |
---|---|

Rank | 4 |

Type | Noble |

Space | Spherical |

Notation | |

Bowers style acronym | Pedit |

Coxeter diagram | m5o2m5o |

Elements | |

Cells | 25 tetragonal disphenoids |

Faces | 50 isosceles triangles |

Edges | 10+25 |

Vertices | 10 |

Vertex figure | Pentagonal tegum |

Measures (based on pentagons of edge length 1) | |

Edge lengths | Base (10): 1 |

Lacing (25): | |

Circumradius | |

Inradius | |

Central density | 1 |

Related polytopes | |

Army | Pedit |

Regiment | Pedit |

Dual | Pentagonal duoprism |

Conjugate | Pentagrammic duotegum |

Abstract & topological properties | |

Euler characteristic | 0 |

Orientable | Yes |

Properties | |

Symmetry | H_{2}≀S_{2}, order 200 |

Convex | Yes |

Nature | Tame |

The ratio between the longest and shortest edges is 1: ≈ 1:1.20300.

## Vertex coordinatesEdit

The vertices of a pentagonal duotegum based on two pentagons of edge length 1, centered at the origin, are given by: