# Triakis icosahedral tegum

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Triakis icosahedral tegum | |
---|---|

Rank | 4 |

Type | Uniform dual |

Notation | |

Coxeter diagram | m2m5m3o () |

Elements | |

Cells | 120 sphenoids |

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

Edges | 24+30+40+60 |

Vertices | 2+12+20 |

Vertex figure | 2 triakis icosahedra, 12 decagonal tegums, 20 triangular tegums |

Measures (edge length 1) | |

Central density | 1 |

Related polytopes | |

Dual | Truncated dodecahedral prism |

Conjugate | Great triakis icosahedral tegum |

Abstract & topological properties | |

Euler characteristic | 0 |

Orientable | Yes |

Properties | |

Symmetry | H3×A1, order 240 |

Convex | Yes |

Nature | Tame |

The **triakis icosahedral tegum**, also known as the **triakis icosahedral 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 triakis icosahedron.

In the variant obtained as the dual of the uniform truncated dodecahedral prism, if the short edges of the triakis icosahedron have length 1, its height is .