# Truncated square prismatic honeycomb

Truncated square prismatic honeycomb | |
---|---|

Rank | 4 |

Type | uniform |

Space | Euclidean |

Notation | |

Bowers style acronym | Tassiph |

Coxeter diagram | |

Elements | |

Cells | N cubes, N octagonal prisms |

Faces | N+2N+4N squares, N octagons |

Edges | 2N+4N+4N |

Vertices | 4N |

Vertex figure | Notch, edge lengths √2+√2 (two equatorial edges) and √2 (remaining edges) |

Related polytopes | |

Army | Tassiph |

Regiment | Tassiph |

Dual | Tetrakis square prismatic honeycomb |

Conjugate | Quasitruncated square prismatic honeycomb |

Abstract & topological properties | |

Orientable | Yes |

Properties | |

Symmetry | R_{3}❘W_{2} |

Convex | Yes |

The **truncated square prismatic honeycomb**, or **tassiph**, is a convex uniform honeycomb. 2 cubes and 4 octagonal prisms join at each vertex of this honeycomb. As the name suggests, it is the honeycomb product of the truncated square tiling and the apeirogon.

This honeycomb can be alternated into a snub square antiprismatic honeycomb, although it cannot be made uniform. If all octagons are alternated into long rectangles, the result is a cantic bisnub square prismatic honeycomb, and if only half of the octagons are alternated into long rectangles, the result is a edge-snub square prismatic honeycomb, which are nonuniform. Finally, if the octagonal prisms are reduced to long square prisms and the remaining cells are dissected, the result is a distorted cubic honeycomb.

## Vertex coordinates[edit | edit source]

Coordinates for the vertices of a truncated square prismatic honeycomb of edge length 1 are given by all permutations of

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

## Representations[edit | edit source]

A truncated square prismatic honeycomb has the following Coxeter diagrams:

## External links[edit | edit source]

- Klitzing, Richard. "tassiph".

- Wikipedia Contributors. "Truncated square prismatic honeycomb".