# 9-simplex

The **9-simplex**, also called the **decayotton**, or **day**, is the simplest possible non-degenerate 9-polytope. The full symmetry version has 10 regular 8-simplices as facets, joining 3 to a 6-simplex peak and 9 to a vertex, and is one of the 3 regular 9-polytopes. It is the 9-dimensional simplex.

9-simplex | |
---|---|

Rank | 9 |

Type | Regular |

Notation | |

Bowers style acronym | Day |

Coxeter diagram | x3o3o3o3o3o3o3o3o () |

Schläfli symbol | {3,3,3,3,3,3,3,3} |

Tapertopic notation | 1^{8} |

Elements | |

Yotta | 10 enneazetta |

Zetta | 45 octaexa |

Exa | 120 heptapeta |

Peta | 210 hexatera |

Tera | 252 pentachora |

Cells | 210 tetrahedra |

Faces | 120 triangles |

Edges | 45 |

Vertices | 10 |

Vertex figure | 8-simplex, edge length 1 |

Measures (edge length 1) | |

Circumradius | |

Inradius | |

Hypervolume | |

Diyottal angle | |

Height | |

Central density | 1 |

Number of external pieces | 10 |

Level of complexity | 1 |

Related polytopes | |

Army | Day |

Regiment | Day |

Dual | 9-simplex |

Conjugate | None |

Abstract & topological properties | |

Flag count | 3628800 |

Euler characteristic | 2 |

Orientable | Yes |

Properties | |

Symmetry | A_{9}, order 3628800 |

Flag orbits | 1 |

Convex | Yes |

Nature | Tame |

## Vertex coordinates edit

The vertices of a regular 9-simplex of edge length 1, centered at the origin, are given by:

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

Much simpler coordinates can be given in ten dimensions, as all permutations of:

- .

## External links edit

- Klitzing, Richard. "day".
- Wikipedia contributors. "9-simplex".