# Toroidal icosahedron faceting

Jump to navigation
Jump to search

Toroidal icosahedron faceting | |
---|---|

Rank | 3 |

Type | Toroid, orbiform |

Space | Spherical |

Notation | |

Bowers style acronym | Toif |

Elements | |

Faces | 6 triangles, 6 pentagons |

Edges | 6+6+12 |

Vertices | 6+6 |

Measures (edge length 1) | |

Circumradius | |

Central density | 0 |

Related polytopes | |

Convex hull | Icosahedron |

Convex core | Gyroelongated triangular bipyramid |

Abstract & topological properties | |

Flag count | 96 |

Euler characteristic | 0 |

Orientable | Yes |

Genus | 1 |

Properties | |

Symmetry | (G_{2}×A_{1})/2, order 12 |

Convex | No |

The **toroidal icosahedron faceting** or **toif**, also called the **crazy tube**, is an orbiform toroid. As its name suggests, it is a faceting of the icosahedron.

It has the fewest faces and vertices of any known regular faced toroid, with 12 of each. However is not a Stewart toroid as it self-intersects. The record for the fewest faces of a Stewart toroid is 21, with the tunnelled elongated triangular cupola and the record for the fewest vertices is 15, with the tortuous tunnel.

## Vertex coordinates[edit | edit source]

Its vertex coordinates are the same as those of the icosahedron.

## Gallery[edit | edit source]

## External links[edit | edit source]

- Bowers, Jonathan. "Batch 2: Ike and Sissid Facetings" (#10 under ike).

- McNeil, Jim. "Simple Stewart toroids".
- Klitzing, Richard. "ike-facetings".