# Chamfered dodecahedron

Chamfered dodecahedron | |
---|---|

Rank | 3 |

Type | Near-miss |

Notation | |

Bowers style acronym | Chado |

Conway notation | cD t5daD |

Elements | |

Faces | 12 pentagons, 30 rectangular-symmetric hexagons |

Edges | 60+60 |

Vertices | 20+60 |

Vertex figures | 20 equilateral triangles |

60 isosceles triangles | |

Measures (edge length 1) | |

Dihedral angles | 5-6: |

6-6: 144° | |

Central density | 1 |

Number of external pieces | 42 |

Level of complexity | 4 |

Related polytopes | |

Army | Chamfered dodecahedron |

Regiment | Chamfered dodecahedron |

Dual | Pentakis icosidodecahedron |

Conjugate | None |

Abstract & topological properties | |

Flag count | 480 |

Euler characteristic | 2 |

Surface | Sphere |

Orientable | Yes |

Genus | 0 |

Properties | |

Symmetry | H_{3}, order 120 |

Flag orbits | 4 |

Convex | Yes |

Nature | Tame |

The **chamfered dodecahedron** (OBSA: **chado**), also known as the **order-5 truncated rhombic triacontahedron**, is one of the near-miss Johnson solids. It has 12 pentagons and 30 hexagons as faces, and 80 order-3 vertices divided into two sets of 20 and 60 each. It can be made equilateral, but the hexagons have two angle sizes.

The hexagonal faces have angles of on one pair of opposite vertices, and angles of on the four remaining vertices.

The canonical variant with midradius 1 has two edge lengths: one of length and the other of length with the same dihedral angles as the equilateral variant.

It can also be viewed as an order-5-truncated rhombic triacontahedron, or as an icosahedrally-symmetric Goldberg polyhedron of index (2,0).

It is the convex core of the uniform rhombidodecadodecahedron.

## Vertex coordinates[edit | edit source]

This polytope is missing vertex coordinates. (April 2024) |

## External links[edit | edit source]

- Klitzing, Richard. "chado".
- Wikipedia contributors. "Chamfered dodecahedron".
- McCooey, David. "Chamfered Dodecahedron (all edges equal)"