# Cake pan

(Redirected from Tunnelled elongated triangular cupola)

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Cake pan | |
---|---|

Rank | 3 |

Type | Quasi-convex Stewart toroid |

Space | Spherical |

Notation | |

Stewart notation | Q_{3}P_{6}/P_{3}Q_{3} |

Elements | |

Faces | 3+3+3+3+3 squares, 3+3 triangles |

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

Vertices | 3+3+6+6 |

Measures (edge length 1) | |

Volume | |

Surface area | |

Related polytopes | |

Convex hull | Elongated triangular cupola |

Abstract & topological properties | |

Flag count | 156 |

Euler characteristic | 0 |

Surface | Torus |

Orientable | Yes |

Genus | 1 |

Properties | |

Symmetry | A_{2}×I, order 6 |

Convex | No |

The **cake pan** is a quasi-convex Stewart toroid. It is a tunnelling of a elongated triangular cupola by a triangular cupola and a triangular prism.

It has the fewest faces of any known Stewart toroid with 21 faces.

## Vertex coordinates[edit | edit source]

A cake pan with edge length 1 has the following vertex coordinates:

- ,
- ,
- ,
- .

## Gallery[edit | edit source]

## External links[edit | edit source]

- McNeil, Jim. "Simple Stewart toroids".

## Bibliography[edit | edit source]

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