# Icositetrachoric prism

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Icositetrachoric prism | |
---|---|

File:Icositetrachoric prism.png | |

Rank | 5 |

Type | Uniform |

Notation | |

Bowers style acronym | Icope |

Coxeter diagram | x x3o4o3o () |

Elements | |

Tera | 24 octahedral prisms, 2 icositetrachora |

Cells | 96 triangular prisms, 48 octahedra |

Faces | 192 triangles, 96 squares |

Edges | 24+192 |

Vertices | 48 |

Vertex figure | Cubic pyramid, edge lengths 1 (base), √2 (legs) |

Measures (edge length 1) | |

Circumradius | |

Hypervolume | 2 |

Diteral angles | Ope–trip–ope: 120° |

Ico–oct–ope: 90° | |

Height | 1 |

Central density | 1 |

Number of external pieces | 26 |

Level of complexity | 5 |

Related polytopes | |

Army | Icope |

Regiment | Icope |

Dual | Icositetrachoric tegum |

Conjugate | None |

Abstract & topological properties | |

Flag count | 11520 |

Euler characteristic | 2 |

Orientable | Yes |

Properties | |

Symmetry | F_{4}×A_{1}, order 2304 |

Convex | Yes |

Nature | Tame |

The **icositetrachoric prism** or **icope** is a prismatic uniform polyteron that consists of 2 icositetrachora and 24 octahedral prisms. 1 icositetrachoron and 6 octahedral prisms join at each vertex. As the name suggests, it is a prism based on the icositetrachoron, which also makes it a convex segmentoteron.

The icositetrachoric prism contains the vertices of a regular penteract.

## Vertex coordinates[edit | edit source]

The vertices of an icositetrachoric prism of edge length 1 are given by all permutations and sign changes of the first four coordinates of:

## External links[edit | edit source]

- Klitzing, Richard. "Icope".