# Rectified decachoron

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Rectified decachoron | |
---|---|

Rank | 4 |

Type | Isogonal |

Notation | |

Bowers style acronym | Redeca |

Coxeter diagram | xo3od3do3ox&#zh |

Elements | |

Cells | 30 tetragonal disphenoids, 10 rectified truncated tetrahedra |

Faces | 120 isosceles triangles, 20 triangles, 20 hexagons |

Edges | 60+120 |

Vertices | 60 |

Vertex figure | Wedge |

Measures (short edge length 1) | |

Edge lengths | Edges of triangles (60): 1 |

Lacing edges (120): | |

Circumradius | |

Central density | 1 |

Related polytopes | |

Army | Redeca |

Regiment | Redeca |

Dual | Joined bidecachoron |

Abstract & topological properties | |

Euler characteristic | 0 |

Orientable | Yes |

Properties | |

Symmetry | A_{4}×2, order 240 |

Convex | Yes |

Nature | Tame |

The **rectified decachoron** is a convex isogonal polychoron that consists of 10 rectified truncated tetrahedra and 30 tetragonal disphenoids. 3 rectified truncated tetrahedra and 2 tetragonal disphenoids join at each vertex. It can be formed by rectifying the decachoron.

It can also be formed as the convex hull of 2 oppositely oriented semi-uniform variants of the small rhombated pentachoron, where the edges of the octahedra are 3 times the length of the other edges. It is one of five polychora (including two transitional cases) formed from two small rhombated pentachora, and is the transitional point between the small birhombatodecachoron and great birhombatodecachoron.

The ratio between the longest and shortest edges is 1: ≈ 1:1.73205.

## External links[edit | edit source]

- Bowers, Jonathan. "Pennic and Decaic Isogonals".

- Klitzing, Richard. "redeca".