# Great cuboctachoron

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Great cuboctachoron | |
---|---|

Rank | 4 |

Type | Scaliform |

Notation | |

Bowers style acronym | Gaco |

Elements | |

Cells | 16 cubes 8 blends of 2 octagrammic prisms |

Faces | 32+64 squares 16 octagrams |

Edges | 128 3-fold 32 4-fold |

Vertices | 64 |

Vertex figure | Butterfly pyramid, edge lengths √2, √2-√2, √2, √2-√2 (base), √2 (legs) |

Measures (edge length 1) | |

Circumradius | |

Central density | 0 |

Related polytopes | |

Army | Tat |

Regiment | Gittith subregiment |

Conjugate | Chasmic cuboctachoron |

Abstract & topological properties | |

Orientable | Yes |

Properties | |

Symmetry | B_{2}≀S_{2}, order 128 |

Convex | No |

Nature | Tame |

The **great cuboctachoron** or **gaco** is a scaliform polychoron that consists of 16 cubes and 8 blends of 2 octagrammic prisms. Two cubes and three blends of 2 octagrammic prisms meet at each vertex.

It can be formed as a blend of a great spinoprismatotesseractioctachoron and an octagrammic diorthoprism.

It has the same vertex figure as the great rhombihexahedral prism; the equilateral triangles still correspond to cubes, but the butterfly corresponds instead to a great rhombihexahedron and the isosceles triangles to octagrammic prisms.

This polychoron is in a subregiment of gittith, as it has its vertices and some but not all of its edges.

## External links[edit | edit source]

- Bowers, Jonathan. "Category S2: Podary Scaliforms" (#S20).