# Petrial great stellated dodecahedron

The **petrial great stellated dodecahedron** is a regular skew polyhedron and is the Petrie dual of the great stellated dodecahedron, and so it shares both of its vertices and edges with the great stellated dodecahedron. It consists of 6 skew decagrams and has an Euler characteristic of -4.

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

Rank | 3 |

Type | Regular |

Space | Spherical |

Notation | |

Schläfli symbol | ^{[1]} |

Elements | |

Faces | 6 skew decagrams |

Edges | 30 |

Vertices | 20 |

Vertex figure | Triangle |

Related polytopes | |

Army | Doe |

Regiment | Gissid |

Petrie dual | Great stellated dodecahedron |

Conjugate | Petrial dodecahedron |

Convex hull | Dodecahedron |

Abstract & topological properties | |

Flag count | 120 |

Euler characteristic | -4 |

Schläfli type | {10,3} |

Orientable | No |

Genus | 6 |

Properties | |

Convex | No |

## Vertex coordinatesEdit

The vertices of the petrial great stellated dodecahedron are identical to those of the great stellated dodecahedron, which is the regiment colonel.

## Related polyhedraEdit

The rectification of the petrial great stellated dodecahedron is the great icosihemidodecahedron, which is uniform.

## External linksEdit

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

## ReferencesEdit

## BibliographyEdit

- McMullen, Peter; Schulte, Egon (1997). "Regular Polytopes in Ordinary Space" (PDF).
*Discrete Computational Geometry*(47): 449–478. doi:10.1007/PL00009304.