# Rectified hexacosichoric prism

(Redirected from Roxip)

Rectified hexacosichoric prism | |
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File:Rectified hexacosichoric prism.png | |

Rank | 5 |

Type | Uniform |

Notation | |

Bowers style acronym | Roxip |

Coxeter diagram | x o5o3x3o () |

Elements | |

Tera | 600 octahedral prisms, 120 icosahedral prisms, 2 rectified hexacosichora |

Cells | 1200+2400 triangular prisms, 1200 octahedra, 240 icosahedra |

Faces | 2400+4800 triangles, 3600 squares |

Edges | 720+7200 |

Vertices | 1440 |

Vertex figure | Pentagonal prismatic pyramid, edge lengths 1 (base), (legs) |

Measures (edge length 1) | |

Circumradius | |

Hypervolume | |

Diteral angles | Ope–trip–ope: |

Ipe–trip–ope: | |

Rox–ike–ipe: 90° | |

Rox–oct–ope: 90° | |

Height | 1 |

Central density | 1 |

Number of external pieces | 722 |

Level of complexity | 15 |

Related polytopes | |

Army | Roxip |

Regiment | Roxip |

Dual | Joined hecatonicosachoric tegum |

Conjugate | Rectified grand hexacosichoric prism |

Abstract & topological properties | |

Euler characteristic | 2 |

Orientable | Yes |

Properties | |

Symmetry | H_{4}×A_{1}, order 28800 |

Convex | Yes |

Nature | Tame |

The **rectified hexacosichoric prism** or **roxip** is a prismatic uniform polyteron that consists of 2 rectified hexacosichora, 120 icosahedral prisms, and 600 octahedral prisms. 1 rectified hexacosichoron, 2 icosahedral prisms, and 5 octahedral prisms join at each vertex. As the name suggests, it is a prism based on the rectified hexacosichoron, which also makes it a convex segmentoteron.

## Vertex coordinates[edit | edit source]

The vertices of a rectified hexacosichoric prism of edge length 1 are given by all permutations of the first four coordinates of:

along with even permutations of the first four coordinates of:

## External links[edit | edit source]

- Klitzing, Richard. "Roxip".