# Rhombic dodecahedral tegum

Rhombic dodecahedral tegum | |
---|---|

Rank | 4 |

Type | Uniform dual |

Notation | |

Coxeter diagram | m2o4m3o () |

Elements | |

Cells | 24 rhombic pyramids |

Faces | 48 scalene triangles, 12 rhombi |

Edges | 12+16+24 |

Vertices | 2+6+8 |

Vertex figure | 2 rhombic dodecahedra, 6 octahedra, 8 triangular tegums |

Measures (edge length 1) | |

Central density | 1 |

Related polytopes | |

Dual | Cuboctahedral prism |

Conjugate | None |

Abstract & topological properties | |

Euler characteristic | 0 |

Orientable | Yes |

Properties | |

Symmetry | B_{3}×A_{1}, order 96 |

Convex | Yes |

Nature | Tame |

The **rhombic dodecahedral tegum**, also called the **rhombic dodecahedral bipyramid**, is a convex isochoric polychoron with 24 rhombic pyramids as cells. As the name sugests, it can be constructed as a tegum based on the rhombic dodecahedron.

In the variant obtained as the dual of the uniform cuboctahedral prism, the height from the top to the bottom vertex is times the edge length of the base rhombic dodecahedron.