# Icositetrafold octaswirlchoron

Icositetrafold octaswirlchoron | |
---|---|

File:Icositetrafold octaswirlchoron.png | |

Rank | 4 |

Type | Isogonal |

Space | Spherical |

Elements | |

Cells | 288 rhombic disphenoids, 192 triangular gyroprisms |

Faces | 1152 scalene triangles, 192 triangles |

Edges | 144+288+576 |

Vertices | 144 |

Vertex figure | Edge-vertical bisected square gyrotegum |

Measures (circumradius 1) | |

Edge lengths | 8-valence (144): |

4-valence (288): | |

3-valence (576): | |

Central density | 1 |

Related polytopes | |

Dual | Cubiswirlic hecatontetracontatetrachoron |

Abstract & topological properties | |

Euler characteristic | 0 |

Orientable | Yes |

Properties | |

Symmetry | B_{3}●I_{2}(24), order 1152 |

Convex | Yes |

Nature | Tame |

The **icositetrafold octaswirlchoron** is an isogonal polychoron with 192 triangular gyroprisms, 288 rhombic disphenoids, and 144 vertices. 8 triangular gyroprisms and 8 rhombic disphenoids join at each vertex. It is the sixth in an infinite family of isogonal octahedral swirlchora.

The ratio between the longest and shortest edges is 1: ≈ 1:3.05006.

## Vertex coordinates[edit | edit source]

Coordinates for the vertices of an icositetrafold octaswirlchoron of circumradius 1, centered at the origin, are given by all permutations of:

defining an icositetrachoron, along with all permutations of:

defining the dual icositetrachoron, along with reflections through the *x*=*y* and *z*=*w* hyperplanes of:

along with reflections through the *x*=*y* and *z*=*w* hyperplanes and with all even sign changes of:

along with reflections through the *x*=*y* and *z*=*w* hyperplanes and with all odd sign changes of:

## Isogonal derivatives[edit | edit source]

Substitution by vertices of these following elements will produce these convex isogonal polychora:

- Triangular gyroprism (192): Icositetrafold cubiswirlchoron
- Triangle (192): Icositetrafold cubiswirlchoron
- Edge (144): Icositetrafold octaswirlchoron