# Octagonally tetrablended quasitruncated tesseract

The **octagonally tetrablended quasitruncated tesseract** or **otbaquitit** is a nonconvex scaliform polychoron that consists of 64 regular tetrahedra and 16 blends of 2 quasitruncated cubes. 2 tetrahedra and 4 blends of 2 quasitruncated cubes join at each vertex.

Octagonally tetrablended quasitruncated tesseract | |
---|---|

Rank | 4 |

Type | Scaliform |

Notation | |

Bowers style acronym | Otbaquitit |

Elements | |

Cells | 64 tetrahedra 16 blends of 2 quasitruncated cubes |

Faces | 256 triangles 64 octagrams |

Edges | 256 3-fold 128 4-fold |

Vertices | 128 |

Vertex figure | Butterfly wedge, edge lengths √2-√2 (short butterfly edges) and 1 (remaining edges) |

Measures (edge length 1) | |

Circumradius | |

Hypervolume | 0 |

Related polytopes | |

Army | Oadet |

Regiment | Otbaquitit |

Conjugate | Octagonally tetrablended truncated tesseract |

Abstract & topological properties | |

Euler characteristic | -16 |

Orientable | Yes |

Properties | |

Symmetry | I2(8)≀S2, order 512 |

Convex | No |

Nature | Tame |

It can be constructed as a blend of 4 quasitruncated tesseracts in the same way ondip is constructed as a blend of 4 sidpith. Its vertex figure is in turn a blend of two vertex figures of the quasitruncated tesseract. It has the same symmetry as the octagonal duoprism.

## Vertex coordinates edit

The vertices of an octagonally tetrablended truncated tesseract of edge length 1 are given by all permutations of:

along with all permutations of the first two and/or last two coordinates of:

The first set of vertices are identical to the vertices of an inscribed quasitruncated tesseract.

## External links edit

- Bowers, Jonathan. "Category S3: Special Scaliforms" (#S35).

- Klitzing, Richard. "otbaquitit".