# Square cupofastegium

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Square cupofastegium | |
---|---|

Rank | 4 |

Type | Segmentotope |

Space | Spherical |

Notation | |

Bowers style acronym | Squicuf |

Coxeter diagram | ox xx4xo&#x |

Elements | |

Cells | 4 tetrahedra, 4 triangular prisms, 1 cube, 2 square cupolas |

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

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

Vertices | 8+8 |

Vertex figures | 8 isosceles trapezoidal pyramids, base edge lengths 1, √2, √2, √2, side edge lengths 1, 1, √2. √2 |

8 sphenoids, edge lengths 1 (3), √2 (2), and √2+√2 (1) | |

Measures (edge length 1) | |

Circumradius | |

Hypervolume | |

Dichoral angles | Tet–3–trip: 150° |

Cube–4–trip: | |

Squacu–8–squacu: 90° | |

Squacu–3–tet: 60° | |

Squacu–4–trip: | |

Cube–4–squacu: 45° | |

Heights | Square atop squacu: |

Cube atop oc: | |

Central density | 1 |

Related polytopes | |

Army | Squicuf |

Regiment | Squicuf |

Dual | Square cupolanotch |

Conjugate | Retrograde square cupofastegium |

Abstract & topological properties | |

Euler characteristic | 0 |

Orientable | Yes |

Properties | |

Symmetry | B_{2}×A_{1}×I, order 16 |

Convex | Yes |

Nature | Tame |

The **square cupofastegium**, or **squicuf**, also sometimes called the **square orthobicupolic ring**, is a CRF segmentochoron (designated K-4.73 on Richard Klitzing's list). It consists of 1 cube, 4 tetrahedra, 4 triangular prisms, and 2 square cupolas.

It has two representations as a segmentochoron: square atop square cupola or cube atop octagon.

The square cupofastegium can be obtained as a cap of the small disprismatotesseractihexadecachoron from one of the 24 cubes with square prism symmetry.

## Vertex coordinates[edit | edit source]

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

- ,
- ,
- .

## Representations[edit | edit source]

A square cupofastegium has the following Coxeter diagrams:

- ox xx4xo&#x (full symmetry)
- xxx4oxo&#x (B
_{2}symmetry only, seen with square atop square cupola)

## External links[edit | edit source]

- Klitzing, Richard. "squicuf".