# Hexagrammic prism

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Hexagrammic prism | |
---|---|

Rank | 3 |

Type | Uniform |

Notation | |

Coxeter diagram | xo3ox xx |

Elements | |

Components | 2 triangular prisms |

Faces | 6 squares, 4 triangles as 2 hexagrams |

Edges | 6+12 |

Vertices | 12 |

Vertex figure | Isosceles triangle, edge lengths 1, √2, √2 |

Measures (edge length 1) | |

Circumradius | |

Volume | |

Dihedral angles | 4–3: 90° |

4–4: 60° | |

Height | 1 |

Central density | 2 |

Number of external pieces | 14 |

Level of complexity | 6 |

Related polytopes | |

Army | Semi-uniform Hip, edge lengths (base), 1 (sides) |

Regiment | * |

Dual | Hexagrammic tegum |

Conjugate | None |

Abstract & topological properties | |

Flag count | 72 |

Orientable | Yes |

Properties | |

Symmetry | G_{2}×A_{1}, order 24 |

Convex | No |

Nature | Tame |

The **hexagrammic prism** or **compound of 2 triangular prisms** is a prismatic uniform polyhedron compound. It consists of 2 hexagrams and 6 squares. Each vertex joins one hexagram and two squares. As the name suggests, it is a prism based on a hexagram.

Its quotient prismatic equivalent is the octahedral prism, which is four-dimensional.

## Vertex coordinates[edit | edit source]

A hexagrammic prism 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 prismatic symmetry and the convex hull is a ditrigonal prism.