# Final stellation of the icosahedron

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Final stellation of the icosahedron | |
---|---|

Rank | 3 |

Type | Noble |

Elements | |

Faces | 20 triangular-symmetric great enneagrams |

Edges | 30+60 |

Vertices | 60 |

Vertex figure | Isosceles triangle |

Measures (unit-edge core icosahedron) | |

Edge lengths | Short edges (30): |

Long edges (60): | |

Edge length ratio | |

Circumradius | |

Volume | |

Central density | 25 |

Number of external pieces | 180 |

Level of complexity | 9 |

Related polytopes | |

Army | Semi-uniform truncated icosahedron |

Dual | Great noble triangular hexecontahedron |

Conjugate | Crennell number 4 stellation of the icosahedron |

Convex core | Icosahedron |

Abstract & topological properties | |

Flag count | 360 |

Euler characteristic | –10 |

Orientable | Yes |

Genus | 6 |

Properties | |

Symmetry | H_{3}, order 120 |

Flag orbits | 3 |

Convex | No |

History | |

Discovered by | Edmond Hess |

First discovered | 1875 |

The **final stellation of the icosahedron**, also known as the **echidnahedron**, is a noble polyhedron that consists of 20 irregular but triangular-symmetric great enneagrams. It is a stellation of the icosahedron.

Its convex hull is a variant of the truncated icosahedron with the same edge ratio as the convex hull of the truncated great dodecahedron.

It appears as the cell of the dual of the pentagonal-prismatic heptacosiicosachoron.

The ratio between the longest and shortest edges is 1: ≈ 1:1.02333, making it a near-miss uniform polyhedron.

## Gallery[edit | edit source]

## External links[edit | edit source]

- Wikipedia contributors. "Final stellation of the icosahedron".
- Verse and Dimensions Wiki Contributors. "Echidnahedron".