# Great icosahedral pyramid

Great icosahedral pyramid | |
---|---|

Rank | 4 |

Type | Segmentotope |

Notation | |

Bowers style acronym | Gikepy |

Coxeter diagram | oo5/2oo3ox&#x |

Elements | |

Cells | 20 tetrahedra, 1 great icosahedron |

Faces | 20+30 triangles |

Edges | 12+30 |

Vertices | 1+12 |

Vertex figures | 1 great icosahedron, edge length 1 |

12 pentagrammic pyramids, edge length 1 | |

Measures (edge length 1) | |

Circumradius | |

Height | |

Related polytopes | |

Army | non-RF Ikepy |

Regiment | Sissidpy |

Dual | Great stellated dodecahedral pyramid |

Conjugate | Icosahedral pyramid |

Abstract & topological properties | |

Euler characteristic | 0 |

Orientable | Yes |

Properties | |

Symmetry | H_{3}×I, order 120 |

Convex | No |

Nature | Tame |

The **great icosahedral pyramid**, or **gikepy**, a non-convex segmentotope. It has 20 regular tetrahedra and 1 regular great icosahedron as cells. As the name suggests, it is a pyramid based on the great icosahedron.

It is the first segment of the grand hexacosichoron in vertex-first orientation.

## External links[edit | edit source]

- Klitzing, Richard. "gikepy".