# 7-2 gyrochoron

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7-2 gyrochoron | |
---|---|

Rank | 4 |

Type | Isotopic |

Space | Spherical |

Elements | |

Cells | 7 bilaterally-symmetric edge-truncated tetrahedra |

Faces | 7 isosceles triangles, 7 kites, 7 mirror-symmetric pentagons |

Edges | 7+7+14 |

Vertices | 7+7 |

Vertex figure | 7+7 phyllic disphenoids |

Measures (edge length 1) | |

Central density | 1 |

Related polytopes | |

Dual | 7-2 step prism |

Abstract & topological properties | |

Euler characteristic | 0 |

Orientable | Yes |

Properties | |

Symmetry | S_{2}(I_{2}(7)-2), order 14 |

Convex | Yes |

Nature | Tame |

The **7-2 gyrochoron**, also known as **mobius 7**, is a convex isochoric polychoron and member of the gyrochoron family with 7 bilaterally-symmetric edge-truncated tetrahedra as cells. It is the simplest gyrochoron after the pentachoron and triangular duoprism, both members of existing families, as well as the only isochoric polychoron with 7 cells. It can also be constructed as the 7-3 gyrochoron. It is also the triangular funk prism.

Each cell of this polychoron has bilateral symmetry, with 2 mirror-symmetric pentagons, 2 kites, and 2 isosceles triangles for faces, and shares a face with every other cell.

## Gallery[edit | edit source]

## Isogonal derivatives[edit | edit source]

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

- Edge-truncated tetrahedron (7): 7-2 step prism
- Mirror-symmetric pentagon (7): 7-2 step prism
- Kite (7): 7-2 step prism
- Isosceles triangle (7): 7-2 step prism
- Edge (7): 7-2 step prism
- Edge (14): 14-2 step prism
- Vertex (7): 7-2 step prism

## External links[edit | edit source]

- Bowers, Jonathan. "Four Dimensional Dice Up To Twenty Sides".