# Small bicantitruncatotetracontoctachoron

Small bicantitruncatotetracontoctachoron | |
---|---|

Rank | 4 |

Type | Isogonal |

Notation | |

Bowers style acronym | Sobcotic |

Coxeter diagram | ao3bc4cb3oa&#zd (c < b+a/2) |

Elements | |

Cells | 288 tetragonal disphenoids, 192 triangular prisms, 576 wedges, 144 ditetragonal trapezoprisms, 48 truncated cubes |

Faces | 384 triangles, 1152 isosceles triangles, 576 rectangles, 1152 isosceles trapezoids, 288 ditetragons |

Edges | 576+576+1152+1152 |

Vertices | 1152 |

Vertex figure | Isosceles triangular antiprism |

Measures (based on two great rhombated icositetrachora of edge length 1) | |

Edge lengths | Lacing edges (1152): |

Remaining edges (576+576+1152): 1 | |

Circumradius | |

Central density | 1 |

Related polytopes | |

Army | Sobcotic |

Regiment | Sobcotic |

Dual | Small bimetatetracontoctachoron |

Abstract & topological properties | |

Euler characteristic | 0 |

Orientable | Yes |

Properties | |

Symmetry | F_{4}×2, order 2304 |

Convex | Yes |

Nature | Tame |

The **small bicantitruncatotetracontoctachoron** or **sobcotic**, also known as the **runcinated tetracontoctachoron** or **runcinated bitetracontoctachoron**, is a convex isogonal polychoron that consists of 48 truncated cubes, 144 ditetragonal trapezoprisms, 192 triangular prisms, 576 wedges, and 288 tetragonal disphenoids. 1 truncated cube, 2 ditetragonal trapezoprisms, 1 triangular prism, 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 less than b+a/2 (producing the transitional bicantitruncatotetracontoctachoron in the limiting case). This includes the convex hull of two uniform great rhombated icositetrachora. The lacing edges generally have length .

The cases where b = c (producing uniform truncated cubic cells) can also be considered the result of expanding the cells of the tetracontoctachoron or its dual bitetracontoctachoron outward and filling in the gaps.

Using the ratio method, the lowest possible ratio between the longest and shortest edges is 1: ≈ 1:1.22930.

## External links[edit | edit source]

- Klitzing, Richard. "sobcotic".