# Disphenoidal enneacontahexachoron

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Disphenoidal enneacontahexachoron | |
---|---|

Rank | 4 |

Type | Uniform dual |

Space | Spherical |

Notation | |

Coxeter diagram | o4m3m3o () |

Elements | |

Cells | 96 digonal disphenoids |

Faces | 96+96 isosceles triangles |

Edges | 24+32+64 |

Vertices | 8+16 |

Vertex figure | 16 triakis tetrahedra, 8 tetrakis hexahedra |

Measures (edge length 1) | |

Dichoral angle | |

Central density | 1 |

Related polytopes | |

Dual | Tesseractihexadecachoron |

Abstract & topological properties | |

Flag count | 2304 |

Euler characteristic | 0 |

Orientable | Yes |

Properties | |

Symmetry | B_{4}, order 384 |

Convex | Yes |

Nature | Tame |

The **disphenoidal enneacontahexachoron** is a convex isochoric polychoron with 96 digonal disphenoids as cells. It can be obtained as the dual of the tesseractihexadecachoron.

It can also be obtained as the convex hull of a tesseract and a hexadecachoron, where the edges of the hexadecachoron are times the length of those of the tesseract. Varying the hexadecachoron's edge length to be anything between and times that of the tesseract gives a fully symmetric variant of this polychoron.

## Variations[edit | edit source]

In addition to the fully symmetric variations, the disphenoidal enneacontahexachoron has isotopic variants with D_{4} symmetry (called the sphenoidal enneacontahexachoron).