# Elongated square gyrobicupola

Elongated square gyrobicupola | |
---|---|

Rank | 3 |

Type | CRF |

Space | Spherical |

Notation | |

Bowers style acronym | Esquigybcu |

Coxeter diagram | oxxx4xxxo&#xt |

Elements | |

Faces | 8 triangles, 2+8+8 squares |

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

Vertices | 8+16 |

Vertex figure | 8+16 isosceles trapezoids, edge lengths 1, √2, √2, √2 |

Measures (edge length 1) | |

Circumradius | |

Volume | |

Dihedral angles | 3–4: |

4–4: 135° | |

Central density | 1 |

Related polytopes | |

Army | Esquigybcu |

Regiment | Esquigybcu |

Dual | Gyrodeltoidal icositetrahedron |

Conjugate | Elongated retrograde square gyrobicupola |

Abstract & topological properties | |

Euler characteristic | 2 |

Surface | Sphere |

Orientable | Yes |

Genus | 0 |

Properties | |

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

Convex | Yes |

Nature | Tame |

The **elongated square gyrobicupola**, also called the **pseudo-rhombicuboctahedron**, is one of the 92 Johnson solids (J_{37}). It consists of 8 triangles and 2+8+8 squares. It can be constructed by inserting an octagonal prism between the two halves of the square gyrobicupola. It can also be constructed from the small rhombicuboctahedron by rotating one of its square cupola segments 45°, and could be called the gyrate rhombicuboctahedron.

It is notable because it has the same set of faces around each vertex (one triangle and three squares), but is not a uniform polyhedron, as it is not actually vertex-transitive. It shares this property with its conjugate, which can be constructed as a gyration of the quasirhombicuboctahedron. The elongated square gyrobicupola is the only convex polyhedron with this property, but it is not known if there are any other nonconvex polyhedra with the property.

## Vertex coordinates[edit | edit source]

An elongated square gyrobicupola of edge length 1 has the following vertices:

## External links[edit | edit source]

- Klitzing, Richard. "esquigybcu".

- Quickfur. "The Elongated Square Gyrobicupola".

- Wikipedia Contributors. "Elongated square gyrobicupola".
- McCooey, David. "Elongated Square Gyrobicupola"