# Hexagrammic antiprism

Hexagrammic antiprism | |
---|---|

Rank | 3 |

Type | Uniform |

Notation | |

Coxeter diagram | |

Elements | |

Components | 2 octahedra |

Faces | 12 triangles, 4 triangles as 2 hexagrams |

Edges | 12+12 |

Vertices | 12 |

Vertex figure | Square, edge length 1 |

Measures (edge length 1) | |

Circumradius | |

Volume | |

Dihedral angle | |

Height | |

Central density | 2 |

Number of external pieces | 38 |

Level of complexity | 11 |

Related polytopes | |

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

Regiment | * |

Dual | Hexagrammic antitegum |

Conjugate | None |

Convex core | Order-6-truncated hexagonal tegum |

Abstract & topological properties | |

Flag count | 96 |

Orientable | Yes |

Properties | |

Symmetry | G_{2}×A_{1}, order 24 |

Convex | No |

Nature | Tame |

The **hexagrammic antiprism**, **compound of two triangular antiprisms**, or **compound of two octahedra**, is a prismatic uniform polyhedron. It consists of 12 triangles and 2 hexagrams. Each vertex joins one hexagram and three triangles. As the name suggests, it is an antiprism based on a hexagram.

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

## Vertex coordinates[edit | edit source]

A hexagrammic antiprism of edge length 1 has vertex coordinates given by:

## Variations[edit | edit source]

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

The case of this variant with golden hexagrams as bases occurs as a combocell type of every baby monster snub.