# Pentagonal-pentagrammic duotegum

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

Rank | 4 |

Type | Uniform dual |

Space | Spherical |

Notation | |

Bowers style acronym | Stapedit |

Coxeter diagram | m5o2m5/2o |

Elements | |

Cells | 25 tetrahedra |

Faces | 25+25 triangles |

Edges | 5+5+25 |

Vertices | 5+5 |

Vertex figure | 5 pentagonal tegums, 5 pentagrammic tegums |

Measures (edge length 1) | |

Inradius | |

Hypervolume | |

Related polytopes | |

Army | Stapedit |

Regiment | Stapedit |

Dual | Pentagonal-pentagrammic duoprism |

Conjugate | Pentagonal-pentagrammic duotegum |

Abstract & topological properties | |

Orientable | Yes |

Properties | |

Symmetry | H_{2}×H_{2}, order 100 |

Convex | No |

Nature | Tame |

The **pentagonal-pentagrammic duotegum**, also known as the **5-5/2 duotegum**, is a duotegum that consists of 25 regular tetrahedra and 10 vertices.

This is one of only two 4D duotegums that can be made to have regular tetrahedral cells and equilateral triangular faces. The other is the square duotegum, which is the regular hexadecachoron.

## Vertex coordinates[edit | edit source]

The vertices of a pentagonal-pentagrammic duotegum of edge length 1 are given by:

## External links[edit | edit source]

- Klitzing, Richard. "stapedit".