# Petrial great dodecahedron

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Petrial great dodecahedron | |
---|---|

Rank | 3 |

Type | Regular |

Space | Spherical |

Notation | |

Schläfli symbol | {5,5/2}^{π}{6,5/2} _{5} |

Elements | |

Faces | 10 skew hexagons |

Edges | 30 |

Vertices | 12 |

Vertex figure | Pentagram |

Measures (edge length 1) | |

Circumradius | |

Related polytopes | |

Regiment | Icosahedron |

Petrie dual | Great dodecahedron |

Conjugate | Petrial small stellated dodecahedron |

Convex hull | Icosahedron |

Abstract properties | |

Flag count | 120 |

Euler characteristic | -8 |

Schläfli type | {6,5} |

Topological properties | |

Orientable | No |

Genus | 10 |

Properties | |

Symmetry | H_{3}, order 120 |

Convex | No |

The **petrial great dodecahedron** is a regular skew polyhedron and the Petrie dual of the great dodecahedron. It consists of 10 skew hexagons, has an Euler characteristic of -8, and it shares the vertices and edges of the icosahedron.

## Vertex coordinates[edit | edit source]

The vertices of a petrial great dodecahedron of edge length 1 centered at the origin are the same as the icosahedron, being all cyclic permutations of:

## Related polyhedra[edit | edit source]

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

## External links[edit | edit source]

Wikipedia Contributors. "Petrie dual".