# Gyroelongated triangular prismatic honeycomb

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Gyroelongated triangular prismatic honeycomb | |
---|---|

Rank | 4 |

Type | uniform |

Space | Euclidean |

Notation | |

Bowers style acronym | Gyetaph |

Elements | |

Cells | 2N triangular prisms, N cubes |

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

Edges | N+2N+2N+2N |

Vertices | 2N |

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

Related polytopes | |

Army | Gyetaph |

Regiment | Gyetaph |

Dual | Elongated gyrohexategmatic honeycomb |

Conjugate | Retrogyroelongated triangular prismatic honeycomb |

Abstract & topological properties | |

Orientable | Yes |

Properties | |

Symmetry | W_{2}❘W_{2}❘W_{2}+ |

Convex | Yes |

The **gyroelongated triangular prismatic honeycomb**, or **gyetaph**, is a convex uniform honeycomb. 4 cubes and 6 triangular prisms join at each vertex of this honeycomb.

It can be thought of as a gyrated triangular prismatic honeycomb with layers of cubes inserted between adjacent layers of triangular prisms, an elongated gyrobifastigial honeycomb with the elongated gyrobifastigia dissected into a cube and two triangular prisms, or an elongated triangular prismatic honeycomb where layers of triangular prisms are rotated by 90º. It shares its vertex figure with the latter.

## External links[edit | edit source]

- Klitzing, Richard. "gyetaph".

- Wikipedia Contributors. "Gyroelongated triangular prismatic honeycomb".