# Pentakis dodecahedral tegum

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Pentakis dodecahedral tegum | |
---|---|

Rank | 4 |

Type | Uniform dual |

Notation | |

Coxeter diagram | m2o5m3m () |

Elements | |

Cells | 120 sphenoids |

Faces | 60+60 isosceles triangles, 120 scalene triangles |

Edges | 24+30+40+60 |

Vertices | 2+12+20 |

Vertex figures | 2 pentakis dodecahedra |

20 hexagonal tegums | |

Measures (edge length 1) | |

Central density | 1 |

Related polytopes | |

Dual | Truncated icosahedral prism |

Conjugate | Great stellapentakis dodecahedral tegum |

Abstract & topological properties | |

Euler characteristic | 0 |

Orientable | Yes |

Properties | |

Symmetry | H_{3}×A_{1}, order 240 |

Convex | Yes |

Nature | Tame |

The **pentakis dodecahedral tegum**, also called the **pentakis dodecahedral bipyramid**, is a convex isochoric polychoron with 120 sphenoids as cells. As the name suggests, it can be constructed as a tegum based on the pentakis dodecahedron.

In the variant obtained as the dual of the uniform truncated icosahedral prism, if the short edges of the pentakis dodecahedron have length 1, its height is .