# Triangular-great rhombicuboctahedral duoprism

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Triangular-great rhombicuboctahedral duoprism | |
---|---|

Rank | 5 |

Type | Uniform |

Notation | |

Bowers style acronym | Tragirco |

Coxeter diagram | x3o x4x3x () |

Elements | |

Tera | 12 triangular-square duoprisms, 8 triangular-hexagonal duoprisms, 6 triangular-octagonal duoprisms, 3 great rhombicuboctahedral prisms |

Cells | 24+24+24 triangular prisms, 36 cubes, 24 hexagonal prisms, 18 octagonal prisms |

Faces | 48 triangles, 36+72+72+72 squares, 24 hexagons, 18 octagons |

Edges | 72+72+72+144 |

Vertices | 144 |

Vertex figure | Mirror-symmetric pentachoron, edge lengths √2, √3, √2+√2 (base triangle), 1 (top edge), √2 (side edges) |

Measures (edge length 1) | |

Circumradius | |

Hypervolume | |

Diteral angles | Tisdip–trip–thiddip: |

Tisdip–trip–todip: 135° | |

Thiddip–trip–todip: | |

Tisdip–cube–gircope: 90° | |

Thiddip–hip–gircope: 90° | |

Todip–op–gircope: 90° | |

Gircope–girco–gircope: 60° | |

Height | |

Central density | 1 |

Number of external pieces | 29 |

Level of complexity | 60 |

Related polytopes | |

Army | Tragirco |

Regiment | Tragirco |

Dual | Triangular-disdyakis dodecahedral duotegum |

Conjugate | Triangular-quasitruncated cuboctahedral duoprism |

Abstract & topological properties | |

Euler characteristic | 2 |

Orientable | Yes |

Properties | |

Symmetry | B_{3}×A_{2}, order 288 |

Convex | Yes |

Nature | Tame |

The **triangular-great rhombicuboctahedral duoprism** or **tragirco** is a convex uniform duoprism that consists of 3 great rhombicuboctahedral prisms, 6 triangular-octagonal duoprisms, 8 triangular-hexagonal duoprisms, and 12 triangular-square duoprisms. Each vertex joins 2 great rhombicuboctahedral prisms, 1 triangular-square duoprism, 1 triangular-hexagonal duoprism, and 1 triangular-octagonal duoprism. It is a duoprism based on a triangle and a great rhombicuboctahedron, which makes it a convex segmentoteron.

## Vertex coordinates[edit | edit source]

The vertices of a triangular-great rhombicuboctahedral duoprism of edge length 1 are given by all permutations of the last three coordinates of:

## External links[edit | edit source]

- Klitzing, Richard. "tragirco".