# Hexagonal-cuboctahedral duoprism

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Hexagonal-cuboctahedral duoprism | |
---|---|

Rank | 5 |

Type | Uniform |

Notation | |

Bowers style acronym | Haco |

Coxeter diagram | x6o o4x3o () |

Elements | |

Tera | 8 triangular-hexagonal duoprisms, 6 square-hexagonal duoprisms, 6 cuboctahedral prisms |

Cells | 48 triangular prisms, 36 cubes, 24 hexagonal prisms, 6 cuboctahedra |

Faces | 48 triangles, 36+144 squares, 12 hexagons |

Edges | 72+144 |

Vertices | 72 |

Vertex figure | Rectangular scalene, edge lengths 1, √2, 1, √2 (base rectangle), √3 (top), √2 (side edges) |

Measures (edge length 1) | |

Circumradius | |

Hypervolume | |

Diteral angles | Thiddip–hip–shiddip: |

Cope–co–cope: 120° | |

Thiddip–trip–cope: 90° | |

Shiddip–cube–cope: 90° | |

Central density | 1 |

Number of external pieces | 20 |

Level of complexity | 20 |

Related polytopes | |

Army | Haco |

Regiment | Haco |

Dual | Hexagonal-rhombic dodecahedral duotegum |

Abstract & topological properties | |

Flag count | 11520 |

Euler characteristic | 2 |

Orientable | Yes |

Properties | |

Symmetry | B_{3}×G_{2}, order 576 |

Convex | Yes |

Nature | Tame |

The **hexagonal-cuboctahedral duoprism** or **haco** is a convex uniform duoprism that consists of 6 cuboctahedral prisms, 6 square-hexagonal duoprisms, and 8 triangular-hexagonal duoprisms. Each vertex joins 2 cuboctahedral prisms, 2 triangular-hexagonal duoprisms, and 2 square-hexagonal duoprisms.

## Vertex coordinates[edit | edit source]

The vertices of a hexagonal-cuboctahedral duoprism of edge length 1 are given by all permutations of the last three coordinates of:

## Representations[edit | edit source]

A hexagonal-cuboctahedral duoprism has the following Coxeter diagrams:

- x6o o4x3o (full symmetry)
- x3x o4x3o (hexagons as ditrigons)
- x6o x3o3x
- x3x x3o3x
- oxx3xxo xxx3xxx&#xt (triangular-hexagonal duoprism || pseudo hexagonal duoprism || gyro triangular-hexagonal duoprism)

## External links[edit | edit source]

- Klitzing, Richard. "haco".