# Tortuous tunnel

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Tortuous tunnel | |
---|---|

Rank | 3 |

Type | Quasi-convex Stewart toroid |

Space | Spherical |

Notation | |

Stewart notation | M, Q _{3}Q_{3}/S_{3}S_{3} |

Elements | |

Faces | 6 squares, 6+6+6 triangles |

Edges | 3+3+3+6+12+12 |

Vertices | 3+6+6 |

Measures (edge length 1) | |

Volume | |

Surface area | |

Related polytopes | |

Convex hull | Triangular orthobicupola |

Abstract & topological properties | |

Flag count | 156 |

Euler characteristic | 0 |

Surface | Torus |

Orientable | Yes |

Genus | 1 |

Properties | |

Symmetry | A_{2}×A_{1}, order 12 |

Convex | No |

The **tortuous tunnel** or **M** is a quasi-convex Stewart toroid. It can be made by excavating 2 octahedra from a triangular orthobicupola. It has the fewest vertices of any known quasi-convex Stewart toroid, with 15.

## Vertex coordinates[edit | edit source]

A tortuous tunnel with edge length 1 has the following vertex coordinates:

- ,
- ,
- ,
- ,
- ,
- .

## Gallery[edit | edit source]

## External links[edit | edit source]

- Doskey, Alex. "Chapter 5 - Simplest (R)(A)(Q)(T) Toroids of genus p=1".
- McNeil, Jim. "Simple Stewart toroids".

## Bibliography[edit | edit source]

- Stewart, Bonnie (1964).
*Adventures Amoung the Toroids*(2 ed.). ISBN 0686-119 36-3.