# Edge-snub trihexagonal prismatic honeycomb

Edge-snub trihexagonal prismatic honeycomb | |
---|---|

Rank | 4 |

Type | Isogonal |

Space | Euclidean |

Notation | |

Coxeter diagram | s∞o2s3s6x |

Elements | |

Cells | 3N wedges, 2N triangular gyroprisms, N ditrigonal trapezoprisms |

Faces | 12N scalene triangles, 2N triangles, 6N isosceles trapezoids, 3N rectangles, N ditrigons |

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

Vertices | 6N |

Vertex figure | Kite-hexagonal orthonotch |

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

Edge lengths | Remaining original eddges (3N): 1 |

Diagonals of original squares (6N+6N): | |

Edges of triangles (6N): | |

Long edges of ditrigons (N): | |

Related polytopes | |

Dual | Trihexagonal isosceles trapezoidal-hexagonal orthowedge honeycomb |

Abstract & topological properties | |

Orientable | Yes |

Properties | |

Symmetry | P_{3}❘W_{2})+ |

Convex | Yes |

Nature | Tame |

The **edge-snub trihexagonal prismatic honeycomb** is an isogonal honeycomb that consists of ditrigonal trapezoprisms, triangular gyroprisms, and wedges. 2 ditrigonal trapezoprisms, 2 triangular gyroprisms, and 6 wedges join at each vertex. It can be obtained as a subsymmetrical faceting of the great rhombitrihexagonal prismatic honeycomb, faceting the dodecagons into ditrigons. However, it cannot be made uniform.

The sectioning facet underneath the alternatingly omitted edge of the prismatic pre-image honeycomb clearly is bistratic (the biwedge), which are subdivided into two wedges.

Using the ratio method, the lowest possible ratio between the longest and shortest edges is 1:*a* ≈ 1:1.32682, where *a* is the second largest real root of 7x^{4}-10x^{3}-10x^{2}+10x+6.

## External links[edit | edit source]

- Klitzing, Richard. "s∞o2s3s6x".