# Retrosphenoverted hexadecatesseractioctachoron

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Retrosphenoverted hexadecatesseractioctachoron | |
---|---|

Rank | 4 |

Type | Uniform |

Space | Spherical |

Notation | |

Bowers style acronym | Rawvhitto |

Coxeter diagram | o4x3x3/2o3*b () |

Elements | |

Cells | 8 cuboctahedra, 16 octahemioctahedra, 8 truncated octahedra |

Faces | 32+64 triangles, 48 squares, 64 hexagons |

Edges | 96+192 |

Vertices | 96 |

Vertex figure | Crossed wedge, edge lengths 1 (2 edges of base rectangle and top edge), √2 (remaining base edges), and √3 (side edges) |

Measures (edge length 1) | |

Circumradius | |

Hypervolume | |

Dichoral angles | Oho–3–co: 120° |

Oho–3–oho: 120° | |

Co–4–toe: 90° | |

Oho–6–toe: 60° | |

Related polytopes | |

Army | Rico |

Regiment | Rico |

Conjugate | None |

Convex core | Tesseract |

Abstract properties | |

Euler characteristic | –16 |

Topological properties | |

Orientable | Yes |

Properties | |

Symmetry | B_{4}, order 384 |

Convex | No |

Nature | Tame |

The **retrosphenoverted hexadecatesseractioctachoron**, or **rawvhitto**, is a nonconvex uniform polychoron that consists of 8 cuboctahedra, 8 truncated octahedra, and 16 octahemioctahedra. 1 cuboctahedron, 2 truncated octahedra, and 2 octahemioctahedra join at each vertex.

## Representations[edit | edit source]

The retrosphenoverted hexadecatesseractioctachoron has the following Coxeter diagrams:

- o4x3x3/2o3*b (full symmetry)
- x3x3o3x3*a3/2*c (D
_{4}symmetry, skewvert)

## Vertex coordinates[edit | edit source]

Its vertices are the same as those of its regiment colonel, the rectified icositetrachoron.

## External links[edit | edit source]

- Bowers, Jonathan. "Category 6: Sphenoverts" (#147).

- Klitzing, Richard. "rawvhitto".