# Gyrobifastigium

Gyrobifastigium | |
---|---|

Rank | 3 |

Type | CRF |

Notation | |

Bowers style acronym | Gybef |

Coxeter diagram | xxo oxx&#xt |

Elements | |

Faces | |

Edges | 2+4+8 |

Vertices | 4+4 |

Vertex figures | 4 isosceles triangles, edge lengths 1, √2, √2 |

4 kites, edge lengths 1 and √2 | |

Measures (edge length 1) | |

Volume | |

Dihedral angles | 4–3 join: 150° |

4–3 prismatic: 90° | |

4–4: 60° | |

Central density | 1 |

Number of external pieces | 8 |

Level of complexity | 7 |

Related polytopes | |

Army | Gybef |

Regiment | Gybef |

Dual | Elongated tetragonal disphenoid |

Conjugate | None |

Abstract & topological properties | |

Flag count | 56 |

Euler characteristic | 2 |

Surface | Sphere |

Orientable | Yes |

Genus | 0 |

Properties | |

Symmetry | (B_{2}×A_{1})/2, order 8 |

Flag orbits | 7 |

Convex | Yes |

Nature | Tame |

The **gyrobifastigium** (OBSA: **gybef**) is one of the 92 Johnson solids (J_{26}). It consists of 4 triangles and 4 squares. It can be constructed by attaching two triangular prisms, seen as digonal cupolas, at one of their square faces so that their opposite edges are perpendicular. As such, it could be considered to be a digonal gyrobicupola.

The gyrobifastigium (with theoretical edge length 1) is the vertex figure of the triangular duoantiprism, which cannot be made uniform, because the Johnson solid variant is not circumscribable.

## Vertex coordinates[edit | edit source]

A gyrobifastigium of edge length 1 has vertices given by the following coordinates:

- ,
- ,
- .

## In vertex figures[edit | edit source]

The gyrobifastigium appears as the vertex figure of the nonuniform triangular duoantiprism. This vertex figure has an edge length of 1, and has no corealmic realization, because the Johnson gyrobifastigium has no circumscribed sphere.

Variants made by changing the two edges perpendicular to the symmetry axis also appear as the vertex figure of the nonuniform duoantiprisms made out of two regular polygons. The symmetry of the gyrofastigium is (B_{2}×A_{1})/2, order 8 if the two polygons are identical, otherwise the symmetry is K_{2}×I, order 4.

## External links[edit | edit source]

- Klitzing, Richard. "gybef".
- Quickfur. "The gyrobifastigium".

- Wikipedia contributors. "Gyrobifastigium".
- McCooey, David. "Gyrobifastigium"