# Transitional bicantitruncatodecachoron

Transitional bicantitruncatodecachoron | |
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File:Transitional bicantitruncatodecachoron.png | |

Rank | 4 |

Type | Isogonal |

Notation | |

Bowers style acronym | Tabcated |

Coxeter diagram | ao3bc3cb3oa&#zd (c = b+a/2) |

Elements | |

Cells | 20 ditrigonal trapezoprisms, 20 triangular trapezorhombihedra, 10 truncated tetrahedra |

Faces | 40 triangles, 120 isosceles trapezoids, 30 squares 40 ditrigons |

Edges | 60+120+120 |

Vertices | 120 |

Vertex figure | Isosceles trapezoidal pyramid |

Measures (edge length 1) | |

Central density | 1 |

Related polytopes | |

Army | Tabcated |

Regiment | Tabcated |

Dual | Transitional bimetadecachoron |

Abstract & topological properties | |

Euler characteristic | 0 |

Orientable | Yes |

Properties | |

Symmetry | A_{4}×2, order 240 |

Convex | Yes |

Nature | Tame |

The **transitional bicantitruncatodecachoron** or **tabcated** is a convex isogonal polychoron that consists of 10 truncated tetrahedra, 20 ditrigonal trapezoprisms, and 20 triangular trapezorhombihedra. 1 truncated tetrahedron, 2 ditrigonal trapezoprisms, and 2 triangular trapezorhombihedra join at each vertex.

It can also be formed as the convex hull of 2 oppositely oriented semi-uniform variants of the great rhombated pentachoron, where if the great rhombated pentachora are of the form a3b3c3o, then c = b+a/2. It is one of five polychora (including two transitional cases) formed from two great rhombated pentachora, and is the transitional point between the small bicantitruncatodecachoron and medial bicantitruncatodecachoron.

Using the ratio method, the lowest possible ratio between the longest and shortest edges is 1: ≈ 1:1.70711.

## External links[edit | edit source]

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