# Möbius-Kantor polygon

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Möbius-Kantor polygon | |
---|---|

Rank | 2 |

Type | Regular |

Space | Complex |

Notation | |

Coxeter diagram | |

Schläfli symbol | |

Elements | |

Edges | 8 3-edges |

Vertices | 8 |

Vertex figure | 3-edge |

Related polytopes | |

Dual | Möbius-Kantor polygon |

Abstract & topological properties | |

Flag count | 24 |

Euler characteristic | 0 |

Configuration symbol | (8_{3}) |

Properties | |

Symmetry | _{3}[3]_{3}, order 24 |

The **Möbius-Kantor polygon** is a regular complex polygon. It has 8 3-edges and 8 vertices.

## Related polytopes[edit | edit source]

The Möbius-Kantor polygon is closely related to the Möbius-Kantor configuration, with the two having the same abstract structure.

If the vertices of the Möbius-Kantor polygon are treated as vertices in rather than , they are identical to those of the hexadecachoron. Additionally if the 3-edges of the Möbius-Kantor polygon are replaced with triangles in Euclidean space they form a symmetric subset of the faces of the hexadecachoron.

The Hessian polyhedron, has the Möbius-Kantor polygon as its faces and vertex figure.

## External links[edit | edit source]

- Wikipedia contributors. "Möbius-Kantor polygon".
- Klitzing, Richard. 3{3}3{3}3