# Triangular-octahedral duoprism

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Triangular-octahedral duoprism | |
---|---|

Rank | 5 |

Type | Uniform |

Notation | |

Bowers style acronym | Troct |

Coxeter diagram | x3o o4o3x () |

Elements | |

Tera | 8 triangular duoprisms, 3 octahedral prisms |

Cells | 12+24 triangular prisms, 3 octahedra |

Faces | 6+24 triangles, 36 squares |

Edges | 18+36 |

Vertices | 18 |

Vertex figure | Square scalene, edge lengths 1 (base square and top edge) and √2 (sides) |

Measures (edge length 1) | |

Circumradius | |

Hypervolume | |

Diteral angles | Triddip–trip–triddip: |

Triddip–trip–ope: 90° | |

Ope–oct–ope: 60° | |

Heights | Oct atop ope: |

Triddip atop gyro triddip: | |

Central density | 1 |

Number of external pieces | 11 |

Level of complexity | 10 |

Related polytopes | |

Army | Troct |

Regiment | Troct |

Dual | Triangular-cubic duotegum |

Conjugate | None |

Abstract & topological properties | |

Flag count | 2880 |

Euler characteristic | 2 |

Orientable | Yes |

Properties | |

Symmetry | B_{3}×A_{2}, order 288 |

Flag orbits | 10 |

Convex | Yes |

Nature | Tame |

The **triangular-octahedral duoprism** or **troct** is a convex uniform duoprism that consists of 3 octahedral prisms and 8 triangular duoprisms. Each vertex joins 2 octahedral prisms and 3 triangular duoprisms. It is a duoprism based on a triangle and an octahedron, which also makes it a convex segmentoteron.

## Vertex coordinates[edit | edit source]

The vertices of a triangular-octahedral duoprism of edge length 1 are given by all permutations and sign changes of the last three coordinates of:

## Representations[edit | edit source]

A triangular-octahedral duoprism has the following Coxeter diagrams:

- x3o o4o3x (full symmetry)
- x3o o3x3o (A
_{3}×A_{2}symmetry, octahedron as tetratetrahedron) - ox oo4oo3xx&#x (BC
_{3}×A_{1}symmetry, octahedron atop octahedral prism) - ox oo3ox3oo&#x (A
_{3}×A_{1}symmetry) - xo3ox xx3oo&#x (A
_{2}×A_{2}axial, triangular duoprism atop gyro triangular duoprism, triangular-triangular antiprismatic duoprism) - ooo4ooo3xxx&#x (BC
_{3}symmery, octahedra seen differently) - ooo3xxx3ooo&#x (A
_{3}symmetry only)

## External links[edit | edit source]

- Klitzing, Richard. "troct".