# Chasmic cuboctachoron

Chasmic cuboctachoron | |
---|---|

Rank | 4 |

Type | Scaliform |

Space | Spherical |

Notation | |

Bowers style acronym | Caco |

Elements | |

Cells | 16 cubes, 8 blends of 2 octagonal prisms |

Faces | 32+64 squares, 16 octagons |

Edges | 32+128 |

Vertices | 64 |

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

Measures (edge length 1) | |

Circumradius | |

Related polytopes | |

Army | Sidpith |

Regiment | Sidpith subregiment |

Conjugate | Great cuboctachoron |

Topological properties | |

Orientable | Yes |

Properties | |

Symmetry | B_{2}≀S_{2}, order 128 |

Convex | No |

Nature | Tame |

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

It can be formed as a blend of a small spinoprismatotesseractioctachoron and an octagonal diorthoprism (a compound of 2 square-octagonal duoprisms). It is also a blend of four such duoprisms, with pairs of octagonal prism cells themselves blending.

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

This polychoron is in a subregiment of the small disprismatotesseractihexadecachoron, as it has its vertices but not all of its edges (specifically, it is missing one class of 32 edges).

## External links[edit | edit source]

- Bowers, Jonathan. "Category S2: Podary Scaliforms" (#S14).