# Hexadecachoric pyramid

Hexadecachoric pyramid | |
---|---|

File:Hexadecachoric pyramid.png | |

Rank | 4 |

Type | Segmentotope |

Notation | |

Bowers style acronym | Hexpy |

Coxeter diagram | oo4oo3oo3ox&#x |

Elements | |

Tera | 16 pentachora, 1 hexadecachoron |

Cells | 16+32 tetrahedra |

Faces | 24+32 triangles |

Edges | 8+24 |

Vertices | 1+8 |

Vertex figures | 1 hexadecachoron, edge length 1 |

8 octahedral pyramids, edge length 1 | |

Measures (edge length 1) | |

Circumradius | |

Hypervolume | |

Height | Point atop hex: |

Central density | 1 |

Related polytopes | |

Dual | Tesseractic pyramid |

Conjugate | None |

Abstract & topological properties | |

Flag count | 2304 |

Euler characteristic | 0 |

Orientable | Yes |

Properties | |

Symmetry | B_{4}×I, order 384 |

Convex | Yes |

Nature | Tame |

The **hexadecachoric pyramid** is a Blind polytope and CRF segmentoteron. It has 8 regular pentachora and 1 regular hexadecachoron as facets. It is a pyramid based on the hexadecachoron.

It is part of an infinite family of Blind polytopes known as the orthoplecial pyramids. It is one of two non-uniform Blind polytopes in five dimensions, the other being the pentachoric bipyramid.

Two hexadecachoric pyramids can be attached at their bases to form a regular triacontaditeron. A hexadecachoric pyramid can be further cut in half to produce two octahedral scalenes.

Apart from being a point atop hexadecachoron, it has an alternate segmentochoron representation as a tetrahedron atop gyro pentachoron seen as a tetrahedral pyramid.

It appears as a facet of the scaliform tridiminished icosiheptaheptacontadipeton.

## Vertex coordinates[edit | edit source]

The vertices of a hexadecachoric pyramid of edge length 1 are given by:

with all permutations of the first 4 coordinates of:

## External links[edit | edit source]

- Klitzing, Richard. "hexpy".