# Quasitruncated dodecadodecahedron

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Quasitruncated dodecadodecahedron | |
---|---|

Rank | 3 |

Type | Uniform |

Notation | |

Bowers style acronym | Quitdid |

Coxeter diagram | x5/3x5x () |

Elements | |

Faces | 30 squares, 12 decagons, 12 decagrams |

Edges | 60+60+60 |

Vertices | 120 |

Vertex figure | Scalene triangle, edge lengths √2, √(5+√5)/2, √(5–√5)/2 |

Measures (edge length 1) | |

Circumradius | |

Volume | 15 |

Dihedral angles | 10/3–4: |

10–10/3: | |

10–4: | |

Central density | -3 |

Number of external pieces | 402 |

Level of complexity | 28 |

Related polytopes | |

Army | Semi-uniform Grid, edge lengths (decagons), (ditrigon-rectangle) |

Regiment | Quitdid |

Dual | Medial disdyakis triacontahedron |

Conjugate | Quasitruncated dodecadodecahedron |

Convex core | Dodecahedron |

Abstract & topological properties | |

Flag count | 720 |

Euler characteristic | -6 |

Orientable | Yes |

Genus | 4 |

Properties | |

Symmetry | H_{3}, order 120 |

Convex | No |

Nature | Tame |

The **quasitruncated dodecadodecahedron** or **quitdid**, also called the **truncated dodecadodecahedron**, is a uniform polyhedron. It consists of 12 decagrams, 12 decagons, and 30 squares, with one of each type of face meeting per vertex. It can be obtained by quasicantitruncation of the small stellated dodecahedron or great dodecahedron, or equivalently by quasitruncating the vertices of a dodecadodecahedron and then adjusting the edge lengths to be all equal.

It can be alternated into the inverted snub dodecadodecahedron after equalizing edge lengths.

## Vertex coordinates[edit | edit source]

A quasitruncated dodecadodecahedron of edge length 1 has vertex coordinates given by all permutations of

along with all even permutations of:

## External links[edit | edit source]

- Bowers, Jonathan. "Polyhedron Category 5: Omnitruncates" (#60).

- Klitzing, Richard. "quitdid".
- Wikipedia contributors. "Truncated dodecadodecahedron".
- McCooey, David. "Truncated Dodecadodecahedron"