# Medial triambic icosahedron

Medial triambic icosahedron | |
---|---|

Rank | 3 |

Type | Uniform dual |

Notation | |

Bowers style acronym | Matai |

Coxeter diagram | m5/3o3o5*a () |

Elements | |

Faces | 20 nonconvex triambi |

Edges | 60 |

Vertices | 12+12 |

Vertex figure | 12 pentagons, 12 pentagrams |

Measures (edge length 1) | |

Inradius | |

Dihedral angle | |

Central density | 4 |

Number of external pieces | 60 |

Related polytopes | |

Dual | Ditrigonary dodecadodecahedron |

Conjugate | Medial triambic icosahedron |

Convex core | Icosahedron |

Abstract & topological properties | |

Flag count | 240 |

Euler characteristic | –16 |

Orientable | Yes |

Genus | 9 |

Properties | |

Symmetry | H_{3}, order 120 |

Flag orbits | 2 |

Convex | No |

Nature | Tame |

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

It appears the same as the great triambic icosahedron.

If its dual, the ditrigonary dodecadodecahedron, 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 .

## Vertex coordinates[edit | edit source]

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

- ,
- .

## Related polytopes[edit | edit source]

The medial triambic icosahedron is an abstractly regular polyhedron. The underlying abstract polytope can be realized as fully regular in 4-dimensional Euclidean space, as either the blended Petrial great dodecahedron or the blended Petrial small stellated dodecahedron.

## External links[edit | edit source]

- Klitzing, Richard. "ditdid".
- Wikipedia contributors. "Medial triambic icosahedron".
- McCooey, David. "Medial Triambic Icosahedron"
- Hartley, Michael. "{6,5}*240b".
- Wedd, N. R9.15'