# Disdyakis triacontahedral tegum

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Disdyakis triacontahedral tegum | |
---|---|

Rank | 4 |

Type | Uniform dual |

Space | Spherical |

Notation | |

Coxeter diagram | m2m5m3m |

Elements | |

Cells | 240 irregular tetrahedra |

Faces | 120+120+120+120 scalene triangles |

Edges | 24+40+60+60+60+60 |

Vertices | 2+12+20+30 |

Vertex figure | 2 disdyakis triacontahedra, 12 decagonal tegums, 20 hexagonal tegums, 30 octahedra |

Measures (edge length 1) | |

Dichoral angle | |

Central density | 1 |

Related polytopes | |

Dual | Great rhombicosidodecahedral prism |

Conjugate | Great disdyakis triacontahedral tegum |

Abstract properties | |

Euler characteristic | 0 |

Topological properties | |

Orientable | Yes |

Properties | |

Symmetry | H3×A1, order 240 |

Convex | Yes |

Nature | Tame |

The **disdyakis triacontahedral tegum**, also called the **disdyakis triacontahedral bipyramid**, is a convex isochoric polychoron with 240 irregular tetrahedra as cells. As the name suggests, it can be constructed as a tegum based on the disdyakis triacontahedron.

In the variant obtained as the dual of the uniform great rhombicosidodecahedral prism, if the shortest edges of the disdyakis triacontahedron have length 1, its height is .