# Triakis tetrahedral tegum

The **triakis tetrahedral tegum**, also called the **triakis tetrahedral bipyramid**, is a convex isochoric polychoron with 24 sphenoids as cells. As the name suggests, it can be constructed as a tegum based on the triakis tetrahedron.

Triakis tetrahedral tegum | |
---|---|

Rank | 4 |

Type | Uniform dual |

Notation | |

Coxeter diagram | m2m3m3o |

Elements | |

Cells | 24 sphenoids |

Faces | 12+12 isosceles triangles, 24 scalene triangles |

Edges | 6+8+8+12 |

Vertices | 2+4+4 |

Vertex figure | 2 triakis tetrahedra, 4 hexagonal tegums, 4 triangular tegums |

Measures (edge length 1) | |

Central density | 1 |

Related polytopes | |

Dual | Truncated tetrahedral prism |

Conjugate | None |

Abstract & topological properties | |

Euler characteristic | 0 |

Orientable | Yes |

Properties | |

Symmetry | A3×A1, order 48 |

Convex | Yes |

Nature | Tame |

In the variant obtained as the dual of the uniform truncated tetrahedral prism, if the triakis tetrahedron's short edge has length 1, its height is .