# Trireplenished great icosahedron

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Trireplenished great icosahedron | |
---|---|

Rank | 3 |

Type | Orbiform |

Notation | |

Bowers style acronym | Targi |

Elements | |

Faces | 1+1+3 triangles, 3 pentagrams |

Edges | 3+3+3+6 |

Vertices | 3+3+3 |

Vertex figures | 3 crossed isosceles trapezoids, edge length 1, 1, 1, (√5-1)/2 |

3+3 isosceles triangles, edge lengths 1, (√5-1)/2, (√5-1)/2 | |

Measures (edge length 1) | |

Circumradius | |

Volume | |

Dihedral angles | 5/2–5/2: |

3-3: | |

3-5/2: | |

Related polytopes | |

Army | Adjacent tridiminished ike |

Regiment | Targi |

Conjugate | Tridiminished icosahedron |

Abstract & topological properties | |

Flag count | 60 |

Orientable | Yes |

Properties | |

Symmetry | A_{2}×I, order 6 |

Convex | No |

Nature | Tame |

The **trireplenished great icosahedron**, or **targi**, is a nonconvex orbiform polyhedron. It consists of 1+1+3 triangles and 3 pentagrams. It can be constructed by removing 3 mutually non-adjacent vertices from a regular great icosahedron.

## Vertex coordinates[edit | edit source]

A trireplenished icosahedron of edge length 1 has the following vertices:

- ,
- ,
- ,
- ,
- ,
- .

## In vertex figures[edit | edit source]

The trireplenished great icosahedron is the vertex figure of the uniform retrosnub disicositetrachoron.

## External links[edit | edit source]

- Bowers, Jonathan. "Batch 2: Ike and Sissid Facetings" (#11 under sissid).

- Klitzing, Richard. "targi".