# Petrial dodecahedron

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

Rank | 3 |

Type | Regular |

Space | Spherical |

Notation | |

Schläfli symbol | |

Elements | |

Faces | 6 skew decagons |

Edges | 30 |

Vertices | 20 |

Vertex figure | Triangle, edge length (1+√5)/2 |

Related polytopes | |

Petrie dual | Dodecahedron |

Conjugate | Petrial great stellated dodecahedron |

Convex hull | Dodecahedron |

Abstract properties | |

Flag count | 120 |

Euler characteristic | -4 |

Schläfli type | {10,3} |

Topological properties | |

Orientable | No |

Genus | 6 |

Properties | |

Convex | No |

The **petrial dodecahedron** is a regular skew polyhedron consisting of 6 skew decagons. The petrial dodecahedron is the Petrie dual of the dodecahedron, so therefore it shares its edges and vertices with the dodecahedron. It has an Euler characteristic of -4.

## Vertex coordinates[edit | edit source]

The vertices of the petrial dodecahedron are identical to those of the dodecahedron, being:

along with all permutations of

## Related polyhedra[edit | edit source]

The rectification of the Petrial dodecahedron is the small icosihemidodecahedron, which is uniform.

## External links[edit | edit source]

- Wikipedia Contributors. "Petrie dual".
- Hartley, Michael. "{10,3}*120b".