# Snub trihexagonal antiprismatic honeycomb

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.

Snub trihexagonal antiprismatic honeycomb | |
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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 |

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

## External links Edit

- Klitzing, Richard. "s∞o2s3s6s".