# Elongated triangular prismatic honeycomb

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Elongated triangular prismatic honeycomb | |
---|---|

Rank | 4 |

Type | Uniform |

Space | Euclidean |

Notation | |

Bowers style acronym | Etoph |

Elements | |

Cells | 2N triangular prisms, N cubes |

Faces | 2N triangles, N+N+2N+2N = 6N squares |

Edges | N+2N+2N+2N = 7N |

Vertices | 2N |

Vertex figure | Irregular pentagonal tegum, edge lengths 1 (two adjacent equatorial edges) and √2 (remaining edges) |

Related polytopes | |

Army | Etoph |

Regiment | Etoph |

Dual | Prismatic pentagonal prismatic honeycomb |

Conjugate | Retroelongated triangular prismatic honeycomb |

Abstract & topological properties | |

Orientable | Yes |

Properties | |

Symmetry | W_{2}❘W_{2}❘W_{2}+ |

Convex | Yes |

The **elongated triangular prismatic honeycomb**, or **etoph**, is a convex uniform honeycomb. 4 cubes and 6 triangular prisms join at each vertex of this honeycomb. As the name suggests, it is the honeycomb product of the elongated triangular tiling and the apeirogon. It can also be thought of as a triangular prismatic honeycomb with layers of cubes inserted between adjacent layers of triangular prisms.

## Vertex coordinates[edit | edit source]

The vertices of an elongated triangular prismatic honeycomb of edge length 1 are given by

where i, j, and k range over the integers.

## External links[edit | edit source]

- Klitzing, Richard. "etoph".

- Wikipedia Contributors. "Elongated triangular prismatic honeycomb".