# Compound of two hexagonal antiprisms

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Compound of two hexagonal antiprisms | |
---|---|

Rank | 3 |

Type | Uniform |

Notation | |

Coxeter diagram | ß2ß12o |

Elements | |

Components | 2 hexagonal antiprisms |

Faces | 24 triangles, 4 hexagons as 2 stellated dodecagons |

Edges | 24+24 |

Vertices | 24 |

Vertex figure | Isosceles trapezoid, edge lengths 1, 1, 1, √3 |

Measures (edge length 1) | |

Circumradius | |

Volume | |

Dihedral angles | 3–3: |

6–3: | |

Height | |

Central density | 2 |

Related polytopes | |

Army | Semi-uniform Twip, edge lengths (base), (sides) |

Regiment | * |

Dual | Compound of two hexagonal antitegums |

Conjugate | Compound of two hexagonal antiprisms |

Abstract & topological properties | |

Flag count | 192 |

Orientable | Yes |

Properties | |

Symmetry | I_{2}(12)×A_{1}, order 48 |

Convex | No |

Nature | Tame |

The **stellated dodecagonal antiprism** or **compound of two hexagonal antiprisms** is a prismatic uniform polyhedron compound. It consists of 2 stellated dodecagons and 24 triangles. Each vertex joins one stellated dodecagon and three triangles. As the name suggests, it is an antiprism based on a stellated dodecagon.

Its quotient prismatic equivalent is the digonal-hexagonal duoantiprism, which is four-dimensional.

## Vertex coordinates[edit | edit source]

Coordinates for the vertices of a stellated dodecagonal antiprism of edge length 1 centered at the origin are given by:

## Variations[edit | edit source]

This compound has variants where the bases are non-regular compounds of two hexagons. In these cases the compound has only hexagonal antiprismatic symmetry and the convex hull is a dihexagonal alterprism.