# Bitruncatotetracontoctachoron

Bitruncatotetracontoctachoron | |
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File:Bitruncatotetracontoctachoron.png | |

Rank | 4 |

Type | Isogonal |

Notation | |

Bowers style acronym | Bitec |

Coxeter diagram | xox3o4ox3ox&#zy |

Elements | |

Cells | 288 tetragonal disphenoids, 576 digonal disphenoids, 48 cubes, 144 square antiprisms |

Faces | 1152+1152 isosceles triangles, 288 squares |

Edges | 192+576+1152 |

Vertices | 384 |

Vertex figure | Hexakis triangular cupola |

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

Edge lengths | Edges of truncated icositetrachora (192+576): 1 |

Lacing edges (1152): | |

Circumradius | |

Central density | 1 |

Related polytopes | |

Army | Bitec |

Regiment | Bitec |

Dual | Biapiculatotetracontoctachoron |

Abstract & topological properties | |

Euler characteristic | 0 |

Orientable | Yes |

Properties | |

Symmetry | F_{4}×2, order 2304 |

Convex | Yes |

Nature | Tame |

The **bitruncatotetracontoctachoron** or **bitec** is a convex isogonal polychoron that consists of 48 cubes, 144 square antiprisms, 288 tetragonal disphenoids, and 576 digonal disphenoids. 1 cube, 3 square antiprisms, 3 tetragonal disphenoids, and 6 digonal disphenoids join at each vertex. It can be obtained as the convex hull of two oppositely oriented truncated icositetrachora.

The bitruncatotetracontoctachoron contains the vertices of a square-octagonal prismantiprismoid and the square double prismantiprismoid.

This polychoron generally has one degree of variation. If the edge length of the truncated icositetrachora are a (those surrounded by truncated octahedra) and b (of cubes), its lacing edges have length and it has circumradius .

Using the ratio method, the lowest possible ratio between the longest and shortest edges is 1: ≈ 1:1.12786.

## Vertex coordinates[edit | edit source]

The vertices of a bitruncatotetracontoctachoron, assuming that the square antiprisms are uniform of edge length 1, centered at the origin, are given by all permutations of:

An alternate set of coordinates, based on two uniform truncated icositetrachora of edge length 1, centered at the origin, are given by all permutations of:

## External links[edit | edit source]

- Klitzing, Richard. "bitec".