# Biambotetrahedral honeycomb

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Biambotetrahedral honeycomb | |
---|---|

Rank | 4 |

Type | Isogonal |

Space | Euclidean |

Notation | |

Bowers style acronym | Bath |

Elements | |

Cells | N rhombitetratetrahedra, N octahedra, 2N+2N triangular antiprisms, 6N rectangular pyramids |

Faces | 6N rectangles, 4N+4N+4N triangles, 12N+12N isosceles triangles |

Edges | 12N+12N+12N |

Vertices | 6N |

Vertex figure | Biwedged rectangular frustum |

Related polytopes | |

Dual | Bijungatotetrahedral honeycomb |

Abstract & topological properties | |

Orientable | Yes |

Properties | |

Symmetry | P4×2 |

Convex | Yes |

Nature | Tame |

The **biambotetrahedral honeycomb** or **bath** is an isogonal honeycomb that consists of rhombitetratetrahedra, octahedra, triangular antiprisms and 6N rectangular pyramids obtained as the union of two rectified tetrahedral-octahedral honeycombs.

This honeycomb cannot be optimized using the ratio method, because the solution (with intended minimal ratio 1: ≈ 1:1.41421) would yield a biambocubic honeycomb instead.

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