# Sphenoverted tesseractitesseractihexadecachoron

Sphenoverted tesseractitesseractihexadecachoron | |
---|---|

Rank | 4 |

Type | Uniform |

Space | Spherical |

Notation | |

Bowers style acronym | Wavitoth |

Coxeter diagram | o3x3o4x4/3*b () |

Elements | |

Cells | 16 octahedra, 8 quasitruncated hexahedra, 8 great cubicuboctahedra |

Faces | 64+64 triangles, 24 squares, 48 octagrams |

Edges | 96+192 |

Vertices | 96 |

Vertex figure | Wedge, edge lengths 1 (base square), √2 (top edge), and √2–√2 (side edges) |

Measures (edge length 1) | |

Circumradius | |

Hypervolume | |

Dichoral angles | Oct–3–quith: 120° |

Gocco–8/3–quith: 90° | |

Gocco–4–gocco: 90° | |

Gocco–3–oct: 60° | |

Related polytopes | |

Army | Srit |

Regiment | Wavitoth |

Conjugate | Retrosphenoverted tesseractitesseractihexadecachoron |

Convex core | Semi-uniform tesseractihexadecachoron |

Abstract & topological properties | |

Euler characteristic | –24 |

Orientable | Yes |

Properties | |

Symmetry | B_{4}, order 384 |

Convex | No |

Nature | Tame |

The **sphenoverted tesseractitesseractihexadecachoron**, or **wavitoth**, is a nonconvex uniform polychoron that consists of 16 regular octahedra, 8 quasitruncated hexahedra, and 8 great cubicuboctahedra. 1 octahedron, 2 quasitruncated hexahedra, and 2 great cubicuboctahedra join at each vertex.

The sphenoverted tesseractitesseractihexadecachoron can be vertex-inscribed into a great distetracontoctachoron and contains the vertices of an octagrammic duoprism and the quasitruncated hexahedral prism.

## Gallery[edit | edit source]

## Vertex coordinates[edit | edit source]

The vertices of a sphenoverted tesseractitesseractihexadecachoron of edge length 1 are given by all permutations of:

## Related polychora[edit | edit source]

The sphenoverted tesseractitesseractihexadecachoron is the colonel of a 7-member regiment. Its other members include the quasirhombated tesseract, great rhombic disoctachoron, great pseudorhombic prismatotesseract, grand quasirhombic prismatotesseract, disprismatointercepted tesseractihexadecachoron, and prismatointercepted tesseractitesseractihexadecachoron.

## External links[edit | edit source]

- Bowers, Jonathan. "Category 6: Sphenoverts" (#221).

- Klitzing, Richard. "wavitoth".