# Small triambic icosahedron

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Small triambic icosahedron | |
---|---|

Rank | 3 |

Type | Uniform dual |

Notation | |

Bowers style acronym | Stai |

Coxeter diagram | m5/2o3o3*a () |

Elements | |

Faces | 20 triambuses |

Edges | 60 |

Vertices | 20+12 |

Vertex figure | 20 triangles, 12 pentagrams |

Measures (edge length 1) | |

Inradius | |

Volume | |

Surface area | |

Dihedral angle | |

Central density | 2 |

Number of external pieces | 60 |

Related polytopes | |

Dual | Small ditrigonary icosidodecahedron |

Conjugate | Great triambic icosahedron |

Convex hull | Non-Catalan Pentakis dodecahedron |

Convex core | Icosahedron |

Abstract & topological properties | |

Flag count | 240 |

Euler characteristic | –8 |

Orientable | Yes |

Genus | 5 |

Properties | |

Symmetry | H_{3}, order 120 |

Convex | No |

Nature | Tame |

The **small triambic icosahedron** is a uniform dual polyhedron. It consists of 20 irregular hexagons, more specifically equilateral triambuses.

If its dual, the small ditrigonary icosidodecahedron, has an edge length of 1, then the edges of the hexagons will measure .

If its convex core, the icosahedron, has an edge length of 1, then the edges of the hexagons will measure .

The hexagons have alternating interior angles of , and .

It is a rare example of a polyhedron with icosahedral symmetry that can be built out of green Zome tools. This is because the compound of five octahedra is its edge stellation.

## Vertex coordinates[edit | edit source]

A small triambic icosahedron with dual edge length 1 has vertex coordinates given by all even permutations of:

## External links[edit | edit source]

- Klitzing, Richard. "stai".

- Wikipedia contributors. "Small triambic icosahedron".
- McCooey, David. "Small Triambic Icosahedron"

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