# Snub trihexagonal antiprismatic honeycomb

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Snub trihexagonal antiprismatic honeycomb | |
---|---|

Rank | 4 |

Type | Isogonal |

Space | Euclidean |

Notation | |

Coxeter diagram | s∞o2s6s3s |

Elements | |

Cells | 12N irregular tetrahedra, 3N rhombic disphenoids, 2N triangular gyroprisms, N hexagonal gyroprisms |

Faces | 12N+12N+12N scalene triangles, 2N triangles, N hexagons |

Edges | 3N+6N+6N+6N+6N+6N |

Vertices | 12N |

Vertex figure | Mirror-symmetric triangular-pentagonal orthobigyrowedge |

Measures (based on great rhombitrihexagonal prismatic honeycomb of edge length 1) | |

Edge lengths | Diagonals of original squares (3N+6N+6N+6N): |

Edges of triangles (6N): | |

Edges of hexagons (6N): | |

Related polytopes | |

Dual | Floret pentagonal antitegmatic honeycomb |

Abstract & topological properties | |

Orientable | Yes |

Properties | |

Symmetry | V_{3}❘W_{2}+ |

Convex | Yes |

Nature | Tame |

The **snub trihexagonal antiprismatic honeycomb** is an isogonal honeycomb that consists of hexagonal gyroprisms, triangular gyroprisms, rhombic disphenoids, and irregular tetrahedra. 2 hexagonal gyroprisms, 2 triangular gyroprisms, 2 rhombic disphenoids, and 8 irregular tetrahedra join at each vertex. It can be obtained through the process of alternating the great rhombitrihexagonal prismatic honeycomb. However, it cannot be made uniform.

Using the ratio method, the lowest possible ratio between the longest and shortest edges is 1: ≈ 1:1.13330.

## External links[edit | edit source]

- Klitzing, Richard. "s∞o2s3s6s".