# 13-5 gyrochoron

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

Rank | 4 |

Type | Isotopic |

Space | Spherical |

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 |

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.

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 | edit source]

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 | edit source]

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