# Great ditrigonary icosidodecahedron

The **great ditrigonary icosidodecahedron** or **gidtid** is a quasiregular uniform polyhedron. It consists of 20 equilateral triangles and 12 pentagons, with three of each joining at a vertex.

Great ditrigonary icosidodecahedron | |
---|---|

Rank | 3 |

Type | Uniform |

Notation | |

Bowers style acronym | Gidtid |

Coxeter diagram | o5x3/2o3*a () |

Elements | |

Faces | 20 triangles, 12 pentagons |

Edges | 60 |

Vertices | 20 |

Vertex figure | Tripod, edge lengths 1 and (1+√5)/2 |

Measures (edge length 1) | |

Circumradius | |

Volume | |

Dihedral angle | |

Central density | 6 |

Number of external pieces | 300 |

Level of complexity | 15 |

Related polytopes | |

Army | Doe, edge length |

Regiment | Sidtid |

Dual | Great triambic icosahedron |

Conjugate | Small ditrigonary icosidodecahedron |

Convex core | Dodecahedron |

Abstract & topological properties | |

Flag count | 240 |

Euler characteristic | –8 |

Orientable | Yes |

Genus | 5 |

Properties | |

Symmetry | H_{3}, order 120 |

Flag orbits | 2 |

Convex | No |

Nature | Tame |

It is a faceting of the small ditrigonary icosidodecahedron, using its 20 triangles along with 12 additional pentagons.

It can be constructed as a holosnub great stellated dodecahedron.

This polyhedron is the vertex figure of the great ditrigonary hexacosihecatonicosachoron.

## Vertex coordinates edit

Its vertices are the same as those of its regiment colonel, the small ditrigonary icosidodecahedron.

## Representations edit

A great ditrigonary icosidodecahedron has the following Coxeter diagrams:

- o5x3/2o3*a ( )
- ß5/2o3o ( ) (as holosnub)

## External links edit

- Bowers, Jonathan. "Polyhedron Category 3: Quasiregulars" (#35).

- Bowers, Jonathan. "Batch 4: Sidtid Facetings" (#3).

- Klitzing, Richard. "gidtid".
- Wikipedia contributors. "Great ditrigonal icosidodecahedron".
- McCooey, David. "Great Ditrigonal Icosidodecahedron"