# Gyroelongated square pyramid

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Gyroelongated square pyramid | |
---|---|

Rank | 3 |

Type | CRF |

Notation | |

Bowers style acronym | Gyesp |

Coxeter diagram | oxo4oox&#xt |

Elements | |

Faces | 4+4+4 triangles, 1 square |

Edges | 4+4+4+8 |

Vertices | 1+4+4 |

Vertex figures | 1 square, edge length 1 |

4 pentagons, edge length 1 | |

4 trapezoids, edge lengths 1, 1, 1, √2 | |

Measures (edge length 1) | |

Volume | |

Dihedral angles | 3–3 join: |

3–3 antiprismatic: | |

3–3 pyramidal: | |

3–4: | |

Central density | 1 |

Number of external pieces | 13 |

Level of complexity | 10 |

Related polytopes | |

Army | Gyesp |

Regiment | Gyesp |

Dual | Order-4 monotruncated tetragonal trapezohedron |

Conjugate | Gyroelongated square pyramid |

Abstract & topological properties | |

Flag count | 80 |

Euler characteristic | 2 |

Surface | Sphere |

Orientable | Yes |

Genus | 0 |

Properties | |

Symmetry | B_{2}×I, order 8 |

Convex | Yes |

Nature | Tame |

The **gyroelongated square pyramid** is one of the 92 Johnson solids (J_{10}). It consists of 4+4+4 triangles and 1 square. It can be constructed by attaching a square antiprism to the base of the square pyramid.

If a second pyramid is attached to the other base of the square antiprism, the result is the gyroelongated square bipyramid.

## Vertex coordinates[edit | edit source]

A gyroelongated square pyramid of edge length 1 has the following vertices:

## External links[edit | edit source]

- Klitzing, Richard. "gyesp".
- Quickfur. "The Gyroelongated Square Pyramid".

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