# Snub bitetrahedral tetracontoctachoron

Snub bitetrahedral tetracontoctachoron | |
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File:Snub bitetrahedral tetracontoctachoron.png | |

Rank | 4 |

Type | Isogonal |

Notation | |

Bowers style acronym | Sebtic |

Elements | |

Cells | 288 phyllic disphenoids, 192 chiral triangular antipodiums, 48 snub tetrahedra |

Faces | 576+576 scalene triangles, 288 isosceles triangles, 192+192 triangles |

Edges | 144+288+576+576 |

Vertices | 288 |

Vertex figure | 11-vertex polyhedron with 2 pentagons, 4 tetragons, and 4 triangles |

Measures (edge length 1) | |

Central density | 1 |

Related polytopes | |

Army | Sebtic |

Regiment | Sebtic |

Dual | Hendecahedral diacosioctacontoctachoron |

Abstract & topological properties | |

Euler characteristic | 0 |

Orientable | Yes |

Properties | |

Symmetry | A_{3}●B_{3}, order 576 |

Convex | Yes |

Nature | Tame |

The **snub bitetrahedral tetracontoctachoron** or **sebtic** is a convex isogonal polychoron that consists of 48 snub tetrahedra, 192 chiral triangular antipodiums and 288 phyllic disphenoids. 2 snub tetrahedra, 4 chiral triangular antipodiums, and 4 phyllic disphenoids join at each vertex. However, it cannot be made uniform.

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 snub bitetrahedral tetracontoctachoron, assuming that the edge length differences are minimized, are given by all even permutations with an even number of sign changes of:

as well as all even permutations with an odd number of sign changes of:

Another set of coordinates for a snub bitetrahedral tetracontoctachoron, assuming that the ratio method is used, are given by all even permutations with an even number of sign changes of:

as well as all even permutations with an odd number of sign changes of: