# Chamfered icosahedron

Jump to navigation
Jump to search

Chamfered icosahedron | |
---|---|

Rank | 3 |

Notation | |

Conway notation | cI t3daD |

Elements | |

Faces | 20 triangles, 30 point-symmetric hexagons |

Edges | 60+60 |

Vertices | 12+60 |

Vertex figures | 12 pentagons |

60 isosceles triangles | |

Measures (edge length 1) | |

Dihedral angles | 3-6: |

6-6: 144° | |

Central density | 1 |

Number of external pieces | 50 |

Level of complexity | 4 |

Related polytopes | |

Army | Chamfered icosahedron |

Regiment | Chamfered icosahedron |

Dual | Triakis 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 icosahedron** is a modification of the icosahedron that can have one edge length but has irregular faces. It has 20 triangles and 30 hexagons as faces, and 12 order-5 vertices that can be thought of as coming from the icosahedron as well as 60 new order-3 vertices.

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

It can be modified such that it has a single inradius, or such that it has a single midradius or "edge radius". The latter version is called the "canonical" version.

It can also be viewed as an order-3-truncated rhombic triacontahedron, or as an icosahedrally-symmetric Goldberg polyhedron.

## Vertex coordinates[edit | edit source]

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

## External links[edit | edit source]

- Klitzing, Richard. "Chamfered ike".
- Wikipedia contributors. "Chamfered icosahedron".
- McCooey, David. "Chamfered Icosahedron (all edges equal)"