# Hexamyriapentachiliapentacositriacontahexapedakon

(Redirected from 16-orthoplex)

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Hexamyriapentachiliapentacositriacontahexapedakon | |
---|---|

Rank | 16 |

Type | Regular |

Space | Spherical |

Notation | |

Coxeter diagram | o4o3o3o3o3o3o3o3o3o3o3o3o3o3o3x |

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

Elements | |

Pedaka | 65536 hexadecatedaka |

Tedaka | 524288 pentadecatradaka |

Tradaka | 1966080 tetradecadoka |

Doka | 4587520 tridecahenda |

Henda | 7454720 dodecadaka |

Daka | 8945664 hendecaxenna |

Xenna | 8200192 decayotta |

Yotta | 5857280 enneazetta |

Zetta | 3294720 octaexa |

Exa | 1464320 heptapeta |

Peta | 512512 hexatera |

Tera | 139776 pentachora |

Cells | 29120 tetrahedra |

Faces | 4480 triangles |

Edges | 480 |

Vertices | 32 |

Vertex figure | Trismyriadischiliaheptacosihexacontoctatedakon, edge length 1 |

Measures (edge length 1) | |

Circumradius | |

Inradius | |

Hypervolume | |

Dihedral angle | |

Height | |

Central density | 1 |

Number of pieces | 65536 |

Level of complexity | 1 |

Related polytopes | |

Army | * |

Regiment | * |

Dual | Hexadekeract |

Conjugate | None |

Abstract properties | |

Euler characteristic | 0 |

Topological properties | |

Orientable | Yes |

Properties | |

Symmetry | B_{16}, order 1371195958099968000 |

Convex | Yes |

Nature | Tame |

The **hexamyriapentachiliapentacositriacontahexapedakon**, also called the **hexadecacross** or **16-orthoplex**, is one of the 3 regular polypedaka. It has 65536 regular hexadecatedaka as facets, joining 4 to a tradakon and 32768 to a vertex in a trismyriadischiliaheptacosihexacontoctatedakal arrangement. It is the 16-dimensional orthoplex. As such it is a diacosipentacontahexazetton duotegum, hexadecachoron tetrategum, and square octategum.

## Vertex coordinates[edit | edit source]

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