# Compound of six tetrahedra (prismatic symmetry)

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Compound of six tetrahedra (prismatic symmetry) | |
---|---|

Rank | 3 |

Type | Uniform |

Elements | |

Components | 6 tetrahedra |

Faces | 24 triangles |

Edges | 12+24 |

Vertices | 24 |

Vertex figure | Equilateral triangle, edge length 1 |

Measures (edge length 1) | |

Circumradius | |

Volume | |

Dihedral angle | |

Height | |

Central density | 6 |

Related polytopes | |

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

Regiment | * |

Dual | Compound of six tetrahedra |

Conjugate | Compound of six tetrahedra |

Abstract & topological properties | |

Flag count | 144 |

Orientable | Yes |

Properties | |

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

Convex | No |

Nature | Tame |

The **compound of six tetrahedra with prismatic symmetry** is a prismatic uniform polyhedron compound. It consists of 24 triangles, with three at each vertex. It is an antiprism based on the compound of six digons.

Its quotient prismatic equivalent is the digonal hexateroorthowedge alterprism, which is eight-dimensional.

## Vertex coordinates[edit | edit source]

Coordinates for the vertices of a compound of six tetrahedra 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 six digons. In these cases the compound has only hexagonal antiprismatic symmetry and the convex hull is a dihexagonal alterprism.