# Great bicantitruncatotetracontoctachoron

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Great bicantitruncatotetracontoctachoron | |
---|---|

Rank | 4 |

Type | Isogonal |

Notation | |

Bowers style acronym | Gobcotic |

Coxeter diagram | ao3bc4cb3oa&#zd (c > b+(2+√2)a) |

Elements | |

Cells | 288 tetragonal disphenoids, 576 wedges, 144 ditetragonal trapezoprisms, 48 great rhombicuboctahedra |

Faces | 1152 isosceles triangles, 1152 isosceles trapezoids, 576 rectangles, 192 ditrigons, 288 ditetragons |

Edges | 576+576+1152+1152 |

Vertices | 1152 |

Vertex figure | Bi-apiculated tetrahedron |

Measures (edge length 1) | |

Central density | 1 |

Related polytopes | |

Army | Gobcotic |

Regiment | Gobcotic |

Dual | Great bimetatetracontoctachoron |

Abstract & topological properties | |

Euler characteristic | 0 |

Orientable | Yes |

Properties | |

Symmetry | F_{4}×2, order 2304 |

Convex | Yes |

Nature | Tame |

The **great bicantitruncatotetracontoctachoron** or **gobcotic** is a convex isogonal polychoron that consists of 48 great rhombicuboctahedra, 144 ditetragonal trapezoprisms, 576 wedges, and 288 tetragonal disphenoids. 2 great rhombicuboctahedra, 2 ditetragonal trapezoprisms, 3 wedges, and 1 tetragonal disphenoid join at each vertex.

[It is one of a total of five distinct polychora (including two transitional cases) that can be obtained as the convex hull of two opposite great rhombated icositetrachora. In this case, if the great rhombated icositetrachora are of the form a3b4c3o, then c must be greater than (producing the truncated tetracontoctachoron in the limiting case). The lacing edges generally have length .