# Octagonal spinoduoprism

Octagonal spinoduoprism | |
---|---|

Rank | 4 |

Type | Uniform |

Notation | |

Bowers style acronym | Ondip |

Elements | |

Cells | 64 tetrahedra, 128 triangular prisms, 64 cubes |

Faces | 256 triangles, 128+128+128 squares |

Edges | 128+128+256 |

Vertices | 128 |

Vertex figure | Blend of two triangular antipodiums, edge lengths 1 (one base each) and √2 (remaining edges) |

Measures (edge length 1) | |

Circumradius | |

Hypervolume | 0 |

Dichoral angles | Tet–3–trip: 150° |

Cube–4–trip: | |

Number of external pieces | 1408 |

Level of complexity | 108 |

Related polytopes | |

Army | Oadet |

Regiment | Ondip |

Conjugate | Great octagonal spinoduoprism |

Abstract & topological properties | |

Euler characteristic | 0 |

Orientable | Yes |

Properties | |

Symmetry | I_{2}(8)≀S_{2}, order 512 |

Convex | No |

Nature | Feral |

The **octagonal spinoduoprism**, or **ondip**, is a nonconvex uniform polychoron that consists of 64 regular tetrahedra, 128 triangular prisms, and 64 cubes. 2 tetrahedra, 6 triangular prisms, and 4 cubes join at each vertex.

It was discovered in March 2006, constructed as a blend of 4 small disprismatotesseractihexadecachora. Its vertex figure is in turn a blend of two vertex figures of the small disprismatotesseractihexadecachoron. It has the same symmetry as the octagonal duoprism.

## Vertex coordinates[edit | edit source]

The vertices of an octagonal spinoduoprism 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 small disprismatotesseractihexadecachoron.

## Related polychora[edit | edit source]

The regiment of the octagonal spinoduoprism contains two other uniform members (the small ditetragonal spinoduoprism and small altersquare duoantiprismoid), a fissary uniform member (the small ditetragonal fissary duoprism, and 10 scaliform members.

## External links[edit | edit source]

- Bowers, Jonathan. "Category 20: Miscellaneous" (#1846).

- Bowers, Jonathan. "How to Make Ondip".

- Klitzing, Richard. "ondip".