# Square pucofastegium

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Square pucofastegium | |
---|---|

Rank | 4 |

Type | Segmentotope |

Notation | |

Bowers style acronym | Squipuf |

Coxeter diagram | ox ox4xx&#x |

Elements | |

Cells | 4 square pyramids, 4 triangular prisms, 2 square cupolas, 1 octagonal prism |

Faces | 8+8 triangles, 1+4+4+8 squares, 2 octagons |

Edges | 4+8+8+8+16 |

Vertices | 4+16 |

Vertex figures | 4 wedges, edge lengths 1 (base square) and √2 (top and side edges) |

16 irregular tetrahedra, edge lengths 1 (2), √2 (3), and √2+√2 (1) | |

Measures (edge length 1) | |

Circumradius | |

Hypervolume | |

Dichoral angles | Squippy–3–trip: 150º |

Squacu–4–trip: | |

Squippy–3–squacu: 120º | |

Squacu–4–squacu: 90º | |

Op–8–squacu: 45º | |

Op–4–squippy: 45º | |

Trip–4–op: | |

Heights | Oc atop squacu: |

Square atop op: | |

Central density | 1 |

Related polytopes | |

Army | Squipuf |

Regiment | Squipuf |

Dual | Square pucolanotch |

Conjugate | Retrograde square pucofastegium |

Abstract & topological properties | |

Euler characteristic | 0 |

Orientable | Yes |

Properties | |

Symmetry | B_{2}×A_{1}×I, order 16 |

Convex | Yes |

Nature | Tame |

The **square pucofastegium**, or **squipuf**, also sometimes called the **square magnabicupolic ring**, is a CRF segmentochoron (designated K-4.105 on Richard Klitzing's list). It consists of 4 triangular prisms, 4 square pyramids, 2 square cupolas, and 1 octagonal prism.

The square pucofastegium occurs as the square-first cap of the small rhombated tesseract. In fact diminishing 8 such caps from the small rhombated tesseract results in the octagonal duoprism.

## Vertex coordinates[edit | edit source]

The vertices of a square pucofastegium with edge length 1 are given by:

## Representations[edit | edit source]

A square pucofastegium has the following Coxeter diagrams:

- ox ox4xx&#x (full symmetry)
- xxx4oxx&#x (BC2 symmetry only, seen with octagon atop square cupola)

## External links[edit | edit source]

- Klitzing, Richard. "squipuf".
- Quickfur. "The Square Magnabicupolic Ring".