# 10-orthoplex

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10-orthoplex | |
---|---|

Rank | 10 |

Type | Regular |

Notation | |

Bowers style acronym | Ka |

Coxeter diagram | x3o3o3o3o3o3o3o3o4o () |

Schläfli symbol | {3,3,3,3,3,3,3,3,4} |

Elements | |

Xenna | 1024 decayotta |

Yotta | 5120 enneazetta |

Zetta | 11520 octaexa |

Exa | 15360 heptapeta |

Peta | 13440 hexatera |

Tera | 8064 pentachora |

Cells | 3360 tetrahedra |

Faces | 960 triangles |

Edges | 180 |

Vertices | 20 |

Vertex figure | Pentacosidodecayotton, edge length 1 |

Measures (edge length 1) | |

Circumradius | |

Inradius | |

Hypervolume | |

Dixennal angle | |

Height | |

Central density | 1 |

Number of external pieces | 1024 |

Level of complexity | 1 |

Related polytopes | |

Army | Ka |

Regiment | Ka |

Dual | Dekeract |

Conjugate | None |

Abstract & topological properties | |

Flag count | 3715891200 |

Euler characteristic | 0 |

Orientable | Yes |

Properties | |

Symmetry | B_{10}, order 3715891200 |

Flag orbits | 1 |

Convex | Yes |

Net count | 26941775019280 |

Nature | Tame |

The **10-orthoplex**, also called the **decacross**, **chiliaicositetraxennon**, or **ka**, is a regular 10-polytope. It has 1024 regular 9-simplices as facets, joining 4 to an 7-simplex peak and 512 to a vertex in a 9-orthoplecial arrangement. It is the 10-dimensional orthoplex. It is also a 5-orthoplex duotegum and square pentategum.

## Vertex coordinates[edit | edit source]

The vertices of a regular chiliaicositetraxennon of edge length 1, centered at the origin, are given by all permutations of:

- .

## External links[edit | edit source]

- Klitzing, Richard. "ka".
- Wikipedia contributors. "10-orthoplex".