# Compound of three cubes (prismatic symmetry)

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Compound of three cubes (prismatic symmetry) | |
---|---|

Rank | 3 |

Type | Uniform |

Elements | |

Components | 3 cubes |

Faces | 12 squares, 6 squares as 2 trisquares |

Edges | 12+24 |

Vertices | 24 |

Vertex figure | Equilateral triangle, edge length √2 |

Measures (edge length 1) | |

Circumradius | |

Volume | 3 |

Dihedral angle | 90° |

Height | 1 |

Central density | 3 |

Number of external pieces | 26 |

Level of complexity | 6 |

Related polytopes | |

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

Regiment | * |

Dual | Compound of three octahedra |

Conjugate | Compound of three cubes |

Abstract & topological properties | |

Flag count | 144 |

Orientable | Yes |

Properties | |

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

Convex | No |

Nature | Tame |

The **trisquare prism** or **compound of three cubes with prismatic symmetry** is a prismatic uniform polyhedron compound. It consists of 2 trisquares and 12 squares. Each vertex joins one trisquare and two squares. As the name suggests, it is a prism based on a trisquare.

Its quotient prismatic equivalent is the 12-4 step prismatic prism, which is five-dimensional.

## Vertex coordinates[edit | edit source]

Coordinates for the vertices of a trisquare prism of edge length 1 centered at the origin are given by: