# Bitetrahedral diacositetracontachoron

Bitetrahedral diacositetracontachoron | |
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File:Bitetrahedral diacositetracontachoron.png | |

Rank | 4 |

Type | Isogonal |

Notation | |

Bowers style acronym | Bittid |

Elements | |

Cells | 1440 phyllic disphenoids, 720 rhombic disphenoids |

Faces | 2880 scalene triangles, 1440 isosceles triangles |

Edges | 480+480+1440 |

Vertices | 240 |

Vertex figure | Chiral ditriakis tetrahedron |

Measures (based on 2 hexacosichora of edge length 1) | |

Edge lengths | 12-valence lacing (480: |

Edges of hexacosichora (1440): 1 | |

6-valence lacing (480): | |

Circumradius | |

Central density | 1 |

Related polytopes | |

Army | Bittid |

Regiment | Bittid |

Dual | Ditruncated-tetrahedral diacositetracontachoron |

Abstract & topological properties | |

Euler characteristic | 0 |

Orientable | Yes |

Properties | |

Symmetry | B_{3}●H_{3}, order 2880 |

Convex | Yes |

Nature | Tame |

The **bitetrahedral diacositetracontachoron** or **bittid**, also known as the **octafold icosidodecaswirlchoron**, is a convex isogonal polychoron that consists of 720 rhombic disphenoids and 1440 phyllic disphenoids. 12 rhombic disphenoids and 24 phyllic disphenoids join at each vertex. However, it cannot be made uniform. It is the second in a series of isogonal icosidodecahedral swirlchora.

It can be formed as the convex hull of two hexacosichora, oriented such that the hull of 2 icositetrachoric sets of 24 vertices from each is a bitetracontoctachoron.

The ratio between the longest and shortest edges is .

## Vertex coordinates[edit | edit source]

Vertex coordinates for a bitetrahedral diacositetracontachoron, created from the vertices of a hexacosichoron of edge length 1, are given by all permutations of:

as well as all even permutations of:

as well as all permutations and even sign changes of:

as well as all permutations and odd sign changes of:

## Isogonal derivatives[edit | edit source]

Substitution by vertices of these following elements will produce these convex isogonal polychora:

- Rhombic disphenoid (720): Snub bitetrahedral diacositetracontachoron