# Elongated square pyramid

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Elongated square pyramid | |
---|---|

Rank | 3 |

Type | CRF |

Notation | |

Bowers style acronym | Esquipy |

Coxeter diagram | oxx4ooo&#xt |

Elements | |

Faces | 4 triangles, 1+4 squares |

Edges | 4+4+4+4 |

Vertices | 1+4+4 |

Vertex figure | 1 square, edge length 1; 4 kites, edge lengths 1 and √2; 4 triangles, edge lengths √2 |

Measures (edge length 1) | |

Volume | |

Dihedral angles | 3–4: |

3–3: | |

4–4: 90° | |

Central density | 1 |

Number of external pieces | 9 |

Level of complexity | 8 |

Related polytopes | |

Army | Esquipy |

Regiment | Esquipy |

Dual | Elongated square pyramid |

Conjugate | Retroelongated square pyramid |

Abstract & topological properties | |

Flag count | 64 |

Euler characteristic | 2 |

Surface | Sphere |

Orientable | Yes |

Genus | 0 |

Properties | |

Symmetry | B_{2}×I, order 8 |

Convex | Yes |

Nature | Tame |

The **elongated square pyramid**, sometimes called an **augmented cube**, is one of the 92 Johnson solids (J_{8}). It consists of 4 triangles and 1+4 squares. It can be constructed by attaching a cube, seen as a square prism, to the base of the square pyramid.

If a second pyramid is attached to the opposite face of the cube, the result is the elongated square bipyramid.

## Vertex coordinates[edit | edit source]

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

## External links[edit | edit source]

- Klitzing, Richard. "esquipy".
- Quickfur. "The Elongated Square Pyramid".

- Weisstein, Eric W. "Elongated Square Pyramid" ("Johnson solid") at MathWorld.

- Wikipedia contributors. "Elongated square pyramid".
- McCooey, David. "Elongated Square Pyramid"