# Snub square prismatic honeycomb

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Snub square prismatic honeycomb | |
---|---|

Rank | 4 |

Type | uniform |

Space | Euclidean |

Notation | |

Bowers style acronym | Sassiph |

Coxeter diagram | x∞o s4s4o |

Elements | |

Cells | 2N triangular prisms, N cubes |

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

Edges | N+2N+4N |

Vertices | 2N |

Vertex figure | Mirror-symmetric pentagonal tegum, edge lengths 1 (two non-adjacent equatorial edges) and √2 (remaining edges) |

Related polytopes | |

Army | Sassiph |

Regiment | Sassiph |

Dual | Cairo pentagonal prismatic honeycomb |

Conjugate | Retrosnub square prismatic honeycomb |

Abstract & topological properties | |

Orientable | Yes |

Properties | |

Symmetry | R_{3}+❘W_{2} |

Convex | Yes |

The **snub square prismatic honeycomb**, or **sassiph**, 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 snub square tiling and the apeirogon.

## Representations[edit | edit source]

A snub square prismatic honeycomb has the following Coxeter diagrams:

- x∞o s4s4o
- x∞x s4s4o
- x∞o s4s4s
- x∞x s4s4s

## External links[edit | edit source]

- Klitzing, Richard. "sassiph".

- Wikipedia Contributors. "Snub square prismatic honeycomb".