# Compound of four octahedra (prismatic symmetry)

Compound of four octahedra (prismatic symmetry) | |
---|---|

Rank | 3 |

Type | Uniform |

Elements | |

Components | 4 octahedra |

Faces | 24 triangles, 8 triangles as 2 tetratriangles |

Edges | 24+24 |

Vertices | 24 |

Vertex figure | Square, edge length 1 |

Measures (edge length 1) | |

Circumradius | |

Volume | |

Dihedral angle | |

Height | |

Central density | 4 |

Related polytopes | |

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

Regiment | * |

Dual | Compound of four cubes |

Conjugate | Compound of four octahedra |

Abstract & topological properties | |

Flag count | 192 |

Orientable | Yes |

Properties | |

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

Convex | No |

Nature | Tame |

The **tetratriangular antiprism** or **compound of four octahedra with prismatic symmetry** is a prismatic uniform polyhedron compound. It consists of 2 tetratriangles and 24 triangles. Each vertex joins one tetratriangle and three triangles. As the name suggests, it is an antiprism based on a tetratriangle.

Its quotient prismatic equivalent is the triangular tetrahedroorthowedge alterprism, which is six-dimensional.

## Vertex coordinates[edit | edit source]

Coordinates for the vertices of a tetratriangular 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 four triangles (seen as two-hexagram compounds). In these cases the compound has only hexagonal prismatic symmetry and the convex hull is a dihexagonal prism.