# Square gyrobicupola

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Square gyrobicupola | |
---|---|

Rank | 3 |

Type | CRF |

Notation | |

Bowers style acronym | Squigybcu |

Coxeter diagram | xxo4oxx&#xt |

Elements | |

Faces | 8 triangles, 2+8 squares |

Edges | 8+8+16 |

Vertices | 8+8 |

Vertex figure | 8 isosceles trapezoids, edge lengths 1, √2, √2, √2; 8 rectangles, edge lengths 1 and √2 |

Measures (edge length 1) | |

Volume | |

Dihedral angles | 3–4 cupolaic: |

4–4: 135° | |

3–4 join: | |

Central density | 1 |

Number of external pieces | 18 |

Level of complexity | 8 |

Related polytopes | |

Army | Squigybcu |

Regiment | Squigybcu |

Dual | Joined square antiprism |

Conjugate | Retrograde square gyrobicupola |

Abstract & topological properties | |

Flag count | 128 |

Euler characteristic | 2 |

Surface | Sphere |

Orientable | Yes |

Genus | 0 |

Properties | |

Symmetry | (I_{2}(8)×A_{1})/2, order 16 |

Convex | Yes |

Nature | Tame |

The **square gyrobicupola** is one of the 92 Johnson solids (J_{29}). It consists of 8 triangles and 2+8 squares. It can be constructed by attaching two square cupolas at their octagonal bases, such that the two square bases are rotated 45° from each other.

It is topologically equivalent to the rectified square antiprism.

If the cupolas are joined such that the bases are in the same orientation, the result is the square orthobicupola.

## Vertex coordinates[edit | edit source]

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

## Related polyhedra[edit | edit source]

An octagonal prism can be inserted between the two halves of the square gyrobicupola to produce the elongated square gyrobicupola.

## External links[edit | edit source]

- Klitzing, Richard. "squigybcu".
- Quickfur. "The Square gyrobicupola".

- Wikipedia contributors. "Square gyrobicupola".
- McCooey, David. "Square Gyrobicupola"