# Hexagonal-snub cubic duoprism

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Hexagonal-snub cubic duoprism | |
---|---|

Rank | 5 |

Type | Uniform |

Notation | |

Bowers style acronym | Hasnic |

Coxeter diagram | x6o s4s3s |

Elements | |

Tera | 8+24 triangular-hexagonal duoprisms, 6 square-hexagonal duoprisms, 6 snub cubic prisms |

Cells | 48+144 triangular prisms, 36 cubes, 12+24+24 hexagonal prisms, 6 snub cubes |

Faces | 48+144 triangles, 36+72+144+144 squares, 24 hexagons |

Edges | 72+144+144+144 |

Vertices | 144 |

Vertex figure | Mirror-symmetric pentagonal scalene, edge lengths 1, 1, 1, 1, √2 (base pentagon), √3 (top edge), √2 (side edges) |

Measures (edge length 1) | |

Circumradius | ≈ 1.67498 |

Hypervolume | ≈ 20.49747 |

Diteral angles | Thiddip–hip–thiddip: ≈ 153.23459° |

Thiddip–hip–shiddip: ≈ 142.98343° | |

Sniccup–snic–sniccup: 120° | |

Thiddip–trip–sniccup: 90° | |

Shiddip–cube–sniccup: 90° | |

Central density | 1 |

Number of external pieces | 44 |

Level of complexity | 50 |

Related polytopes | |

Army | Hasnic |

Regiment | Hasnic |

Dual | Hexagonal-pentagonal icositetrahedral duotegum |

Conjugate | Hexagonal-snub cubic duoprism |

Abstract & topological properties | |

Euler characteristic | 2 |

Orientable | Yes |

Properties | |

Symmetry | B_{3}+×G_{2}, order 288 |

Convex | Yes |

Nature | Tame |

The **hexagonal-snub cubic duoprism** or **hasnic** is a convex uniform duoprism that consists of 6 snub cubic prisms, 6 square-hexagonal duoprisms, and 32 triangular-hexagonal duoprisms of two kinds. Each vertex joins 2 snub cubic prisms, 4 triangular-hexagonal duoprisms, and 1 square-hexagonal duoprism.

## Vertex coordinates[edit | edit source]

The vertices of a hexagonal-snub cubic duoprism of edge length 1 are given by by all even permutations with an even number of sign changes, plus all odd permutations with an odd amount of sign changes, of the last three coordinates of:

where