# Great dodecahedron cone

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Great dodecahedron cone | |
---|---|

Rank | 3 |

Space | Spherical |

Notation | |

Bowers style acronym | Gadcone |

Elements | |

Faces | 5 pentagons, 5 triangles |

Edges | 5+5+10 |

Vertices | 1+5+5 |

Measures (edge length 1) | |

Circumradius | |

Related polytopes | |

Army | Gyepip |

Convex hull | Gyroelongated pentagonal pyramid |

Abstract & topological properties | |

Flag count | 80 |

Euler characteristic | 1 |

Orientable | No |

Genus | 1 |

Properties | |

Symmetry | H_{2}×I, order 10 |

Convex | No |

The **great dodecahedron cone** is an orbiform polyhedron. It is a faceting of the icosahedron with 5 pentagonal and 5 triangular faces.

It is the 5-5-3 acrohedron generated by Green's rules.

## Vertex coordinates[edit | edit source]

It's vertex coordinates are the same as those of the icosahedron with any 1 vertex removed.

## External links[edit | edit source]

- Bowers, Jonathan. "Batch 2: Ike and Sissid Facetings" (#5 under ike).

- McNeil, Jim. "n-n-3 acrohedra".
- Klitzing, Richard. "ike-facetings".