# Bitetrahedral tetracontoctachoron

Bitetrahedral tetracontoctachoron | |
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File:Bitetrahedral tetracontoctachoron.png | |

Rank | 4 |

Type | Isogonal |

Notation | |

Bowers style acronym | Bitac |

Elements | |

Cells | 576 irregular tetrahedra, 288 phyllic disphenoids, 192 triangular pyramids, 144 rhombic disphenoids, 48 tetrahedra |

Faces | 576+576+576 scalene triangles, 576 isosceles triangles, 192 triangles |

Edges | 288+288+288+576 |

Vertices | 192 |

Vertex figure | 15-vertex polyhedron with 26 triangles |

Measures (based on 2 snub icositetrachora of edge length 1) | |

Edge lengths | Lacing edge 1 (288): |

Edges of snub icositetrachora (288+576): 1 | |

Lacing edge 2 (288): | |

Circumradius | |

Central density | 1 |

Related polytopes | |

Army | Bitac |

Regiment | Bitac |

Dual | Pentadecahedral hecatonenneacontadichoron |

Abstract & topological properties | |

Euler characteristic | 0 |

Orientable | Yes |

Properties | |

Symmetry | A_{3}●B_{3}, order 576 |

Convex | Yes |

Nature | Tame |

The **bitetrahedral tetracontoctachoron** or **bitac** is a convex isogonal polychoron that consists of 48 tetrahedra, 144 rhombic disphenoids, 192 triangular pyramids, 288 phyllic disphenoids, and 576 irregular tetrahedra. 1 tetrahedron, 3 rhombic disphenoids, 4 triangular pyramids, 6 phyllic disphenoids, and 12 irregular tetrahedra join at each vertex. However, it cannot be made uniform.

It can be formed as the convex hull of 2 oppositely oriented snub icositetrachora, such that the icosahedra of one snub icositetrachoron align with the tetrahedra of the other.

Using the ratio method, the lowest possible ratio between the longest and shortest edges is 1: ≈ 1:1.48563.

## Vertex coordinates[edit | edit source]

Vertex coordinates for a bitetrahedral tetracontoctachoron, created from the vertices of a snub disicositetrachoron of edge length 1, are given by all even permutations of:

as well as all permutations and even sign changes of:

as well as all permutations and odd sign changes of:

Another set of coordinates for a bitetrahedral tetracontoctachoron, using the ratio method to minimize edge length differences, are given by all even permutations of:

as well as all permutations and even sign changes of:

as well as all permutations and odd sign changes of: