# Hexadecahemidecateron

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Hexadecahemidecateron | |
---|---|

Rank | 5 |

Type | Uniform |

Notation | |

Bowers style acronym | Hehad |

Coxeter diagram | (x3o3o3o3o3/2*b)/2 (/2) |

Elements | |

Tera | 16 pentachora, 5 hexadecachora |

Cells | 80 tetrahedra |

Faces | 80 triangles |

Edges | 40 |

Vertices | 10 |

Vertex figure | Tesseractihemioctachoron, edge length 1 |

Measures (edge length 1) | |

Circumradius | |

Diteral angle | |

Related polytopes | |

Army | Tac |

Regiment | Tac |

Company | Tac |

Dual | Hexadecahemidecacron |

Conjugate | None |

Abstract & topological properties | |

Flag count | 3840 |

Orientable | No |

Properties | |

Symmetry | D_{5}, order 1920 |

Flag orbits | 2 |

Convex | No |

Nature | Tame |

The **hexadecahemidecateron**, or **hehad**, is a uniform hemipolyteron. It has 16 regular pentachora and 5 central hexadecachora as facets, with 8 pentachora and 4 hexadecachora at each vertex in the form of a tesseractihemioctachoron. It is the 5D demicross.

It is a faceting of the triacontaditeron, analogous to how the tetrahemihexahedron is a faceting of the octahedron, and the tesseractihemioctachoron is a faceting of the hexadecachoron. It shares the triacontaditeron's vertices, edges, faces, and cells. The 16 pentachora are half of those of the triacontaditeron, while the hexadecachora are its original vertex figures.

## Vertex coordinates[edit | edit source]

Its vertices are the same as those of its regiment colonel, the triacontaditeron.

## External links[edit | edit source]

- Bowers, Jonathan. "Category 1: Primary Polytera" (#4).

- Klitzing, Richard. "hehad".