# Petrial great icosahedron

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Petrial great icosahedron | |
---|---|

Rank | 3 |

Type | Regular |

Space | Spherical |

Notation | |

Schläfli symbol | |

Elements | |

Faces | 6 skew decagrams |

Edges | 30 |

Vertices | 12 |

Vertex figure | Pentagram, edge length 1 |

Related polytopes | |

Petrie dual | Great icosahedron |

Conjugate | Petrial icosahedron |

Convex hull | Icosahedron |

Abstract properties | |

Flag count | 120 |

Euler characteristic | -12 |

Schläfli type | {10,5} |

Topological properties | |

Orientable | No |

Genus | 14 |

Properties | |

Convex | No |

The **petrial great icosahedron** is a regular skew polyhedron and is the Petrie dual of the great icosahedron, so it shares its vertices and edges with the great icosahedron. It has an Euler characteristic of -12 and consists of 6 skew decagrams.

## Vertex coordinates[edit | edit source]

The vertices of a petrial icosahedron of edge length 1 centered at the origin are the same as the small stellated dodecahedron, its regiment colonel.

## Related polyhedra[edit | edit source]

The rectification of the petrial icosahedron is the great dodecahemidodecahedron, which is uniform.

## External links[edit | edit source]

- Wikipedia Contributors. "Petrie dual".