# Gyrated triangular prismatic honeycomb

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Gyrated triangular prismatic honeycomb | |
---|---|

Rank | 4 |

Type | uniform |

Space | Euclidean |

Notation | |

Bowers style acronym | Gytoph |

Elements | |

Cells | 2N triangular prisms |

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

Edges | 2N+2N |

Vertices | N |

Vertex figure | Snub disphenoid, edge lengths 1 and √2 |

Related polytopes | |

Army | Gytoph |

Regiment | Gytoph |

Dual | Elongated gyrobifastigial honeycomb |

Conjugate | None |

Abstract & topological properties | |

Orientable | Yes |

Properties | |

Symmetry | W_{2}❘W_{2}❘W_{2}+ |

Convex | Yes |

The **gyrated triangular prismatic honeycomb**, or **gytoph**, is a convex noble uniform honeycomb. 12 triangular prisms join at each vertex of this honeycomb.

This honeycomb can be formed from the triangular prismatic honeycomb by rotating alternating layers of triangular prisms by 90°, in a similar way to the gyrobifastigium. Its vertex figure can be constructed from the hexagonal tegum vertex figure of the triangular prismatic honeycomb by cutting it in half along an equatorial square and rotating one half by 90°.

## External links[edit | edit source]

- Klitzing, Richard. "gytoph".

- Wikipedia Contributors. "Gyrated triangular prismatic honeycomb".