# Square orthobicupola

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Square orthobicupola | |
---|---|

Rank | 3 |

Type | CRF |

Notation | |

Bowers style acronym | Squobcu |

Coxeter diagram | xxx4oxo&#xt |

Elements | |

Faces | 8 triangles, 2+8 squares |

Edges | 4+4+8+16 |

Vertices | 8+8 |

Vertex figures | 8 isosceles trapezoids, edge lengths 1, √2, √2, √2 |

8 kites, edge lengths 1 and √2 | |

Measures (edge length 1) | |

Volume | |

Dihedral angles | 3–4: |

4–4 cupolaic: 135° | |

3–3: | |

4–4 join: 90° | |

Central density | 1 |

Number of external pieces | 18 |

Level of complexity | 8 |

Related polytopes | |

Army | Squobcu |

Regiment | Squobcu |

Dual | Deltotrapezohedral hexadecahedron |

Conjugate | Retrograde square orthobicupola |

Abstract & topological properties | |

Flag count | 128 |

Euler characteristic | 2 |

Surface | Sphere |

Orientable | Yes |

Genus | 0 |

Properties | |

Symmetry | B_{2}×A_{1}, order 16 |

Convex | Yes |

Nature | Tame |

The **square orthobicupola** is one of the 92 Johnson solids (J_{28}). 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 in the same orientation.

If the cupolas are joined such that the bases are rotated 45°, the result is the square gyrobicupola.

## Vertex coordinates[edit | edit source]

A square orthobicupola 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 orthobicupola to produce the elongated square orthobicupola, better known as the uniform small rhombicuboctahedron.

## External links[edit | edit source]

- Klitzing, Richard. "squobcu".
- Quickfur. "The Square Orthobicupola".

- Wikipedia contributors. "Square orthobicupola".
- McCooey, David. "Square Orthobicupola"