# 13-5 gyrochoron

The **13-5 gyrochoron**, also known as the **tridecachoron**, is a convex isochoric polychoron and member of the gyrochoron family with 13 prodigonal antiprismatic symmetric elongated gyrobifastigia as cells. It is also the pentagonal funk prism.

13-5 gyrochoron | |
---|---|

Rank | 4 |

Type | Isotopic |

Elements | |

Cells | 13 prodigonal antiprismatic symmetric elongated gyrobifastigia |

Faces | 26 kites, 26 mirror-symmetric pentagons |

Edges | 26+52 |

Vertices | 13+26 |

Vertex figure | 26 phyllic disphenoids, 13 tetragonal disphenoids |

Measures (edge length 1) | |

Central density | 1 |

Related polytopes | |

Dual | 13-5 step prism |

Abstract & topological properties | |

Euler characteristic | 0 |

Orientable | Yes |

Properties | |

Symmetry | S_{2}(I_{2}(13)-5)×2I, order 52 |

Convex | Yes |

Nature | Tame |

Each cell of this polychoron has prodigonal antiprismatic symmetry, with 4 mirror-symmetric pentagons and 4 kites for faces.

Compared to other gyrochora with 13 cells, this polychoron has ionic doubled symmetry, because 13 is a factor of 5^{2}+1 = 26.

## Isogonal derivatives edit

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

- Elongated gyrobifastigium (13): 13-5 step prism
- Mirror-symmetric pentagon (26): Small 13-5 double gyrostep prism
- Kite (26): Small 13-5 double step prism
- Vertex (13): 13-5 step prism

## External links edit

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