# Elongated square bipyramid

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Elongated square bipyramid | |
---|---|

Rank | 3 |

Type | CRF |

Notation | |

Bowers style acronym | Esquidpy |

Coxeter diagram | oxxo4oooo&#xt |

Elements | |

Faces | 8 triangles, 4 squares |

Edges | 4+8+8 |

Vertices | 2+8 |

Vertex figures | 2 squares, edge length 1 |

8 kites, edge lengths 1 and √2 | |

Measures (edge length 1) | |

Volume | |

Dihedral angles | 3–4: |

3–3: | |

4–4: 90° | |

Central density | 1 |

Number of external pieces | 12 |

Level of complexity | 5 |

Related polytopes | |

Army | Esquidpy |

Regiment | Esquidpy |

Dual | Square bifrustum |

Conjugate | None |

Abstract & topological properties | |

Flag count | 80 |

Euler characteristic | 2 |

Surface | Sphere |

Orientable | Yes |

Genus | 0 |

Properties | |

Symmetry | B_{2}×A_{1}, order 16 |

Convex | Yes |

Nature | Tame |

The **elongated square bipyramid** is one of the 92 Johnson solids (J_{15}). It consists of 8 triangles and 4 squares. It can be constructed by inserting a cube, seen as a square prism, between the two pyramidal halves of the regular octahedron, seen as a square bipyramid.

## Vertex coordinates[edit | edit source]

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

- ,
- .

## Representations[edit | edit source]

An elongated square bipyramid has the following Coxeter diagrams:

- oxxo4oooo&#xt (full symmetry)
- oxxo oxxo&#xt (rectangular symmetry)
- xwx xox&#xt (rectangular axial)
- wx ox4oo&#zx (as tegum sum)
- x(xw)x o(qo)o&#xt (edge first)
- qoo oqo xxw&#zx (cuboid symmetry)

## External links[edit | edit source]

- Klitzing, Richard. "esquidpy".
- Quickfur. "The Elongated Square Bipyramid".

- Wikipedia contributors. "Elongated square bipyramid".
- McCooey, David. "Elongated Square Dipyramid"