# Compound of four triangular prisms (prismatic symmetry)

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Compound of four triangular prisms (prismatic symmetry) | |
---|---|

Rank | 3 |

Type | Uniform |

Elements | |

Components | 4 triangular prisms |

Faces | 12 squares, 8 triangles as 2 tetratriangles |

Edges | 12+24 |

Vertices | 24 |

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 | 4 |

Number of external pieces | 26 |

Level of complexity | 6 |

Related polytopes | |

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

Regiment | * |

Dual | Compound of four triangular tegums |

Conjugate | Compound of four triangular prisms |

Abstract & topological properties | |

Flag count | 144 |

Orientable | Yes |

Properties | |

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

Convex | No |

Nature | Tame |

The **tetratriangular prism** or **compound of four triangular prisms with prismatic symmetry** is a prismatic uniform polyhedron compound. It consists of 2 tetratriangles and 12 squares. Each vertex joins one tetratriangle and two squares. As the name suggests, it is a prism based on a tetratriangle.

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

## Vertex coordinates[edit | edit source]

Coordinates for the vertices of a tetratriangular prism 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.