# Small rhombitrihexagonal prismatic honeycomb

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Small rhombitrihexagonal prismatic honeycomb | |
---|---|

Rank | 4 |

Type | Uniform |

Space | Euclidean |

Notation | |

Bowers style acronym | Srothaph |

Coxeter diagram | x∞o2x6o3x () |

Elements | |

Cells | 2N triangular prisms, 3N cubes, N hexagonal prisms |

Faces | 2N triangles, 3N+6N+6N squares, N hexagons |

Edges | 6N+6N+6N |

Vertices | 6N |

Vertex figure | Isosceles trapezoidal tegum, edge lengths 1 and √3 (bases of trapezoid) and √2 (remaining edges) |

Related polytopes | |

Army | Srothaph |

Regiment | Srothaph |

Dual | Deltoidal prismatic honeycomb |

Conjugate | Quasirhombitrihexagonal prismatic honeycomb |

Abstract & topological properties | |

Orientable | Yes |

Properties | |

Symmetry | V_{3}❘W_{2} |

Convex | Yes |

Nature | Tame |

The **small rhombitrihexagonal prismatic honeycomb**, or **srothaph**, also known as the **rhombitrihexagonal prismatic honeycomb**, is a convex uniform honeycomb. 2 triangular prisms, 4 cubes, and 2 hexagonal prisms join at each vertex of this honeycomb. As the name suggests, it is the honeycomb product of the small rhombitrihexagonal tiling and the apeirogon.

## Representations[edit | edit source]

A small rhombitrihexagonal prismatic honeycomb has the following Coxeter diagrams:

- x∞o2x6o3x ()
- x∞x2x6o3x ()
- x∞o2x6s3s ()
- x∞x2x6s3s ()

## External links[edit | edit source]

- Klitzing, Richard. "srothaph".
- Wikipedia contributors. "Rhombitrihexagonal prismatic honeycomb".