# Dodecagonal-great rhombicuboctahedral duoprism

Dodecagonal-great rhombicuboctahedral duoprism | |
---|---|

Rank | 5 |

Type | Uniform |

Notation | |

Bowers style acronym | Twagirco |

Coxeter diagram | x12o x4x3x () |

Elements | |

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

Cells | 144 cubes, 96 hexagonal prisms, 72 octagonal prisms, 24+24+24 dodecagonal prisms, 12 great rhombicuboctahedra |

Faces | 144+288+288+288 squares, 96 hexagons, 72 octagons, 48 dodecagons |

Edges | 288+288+288+576 |

Vertices | 576 |

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

Measures (edge length 1) | |

Circumradius | |

Hypervolume | |

Diteral angles | Gircope–girco–gircope: 150° |

Sitwadip–twip–hitwadip: | |

Sitwadip–twip–otwadip: 135° | |

Hitwadip–twip–otwadip: | |

Sitwadip–cube–gircope: 90° | |

Hitwadip–hip–gircope: 90° | |

Otwadip–op–gircope: 90° | |

Central density | 1 |

Number of external pieces | 38 |

Level of complexity | 60 |

Related polytopes | |

Army | Twagirco |

Regiment | Twagirco |

Dual | Dodecagonal-disdyakis dodecahedral duotegum |

Conjugates | Dodecagrammic-great rhombicuboctahedral duoprism, Dodecagonal-quasitruncated cuboctahedral duoprism, Dodecagrammic-quasitruncated cuboctahedral duoprism |

Abstract & topological properties | |

Euler characteristic | 2 |

Orientable | Yes |

Properties | |

Symmetry | B_{3}×I2(12), order 1152 |

Convex | Yes |

Nature | Tame |

The **dodecagonal-great rhombicuboctahedral duoprism** or **twagirco** is a convex uniform duoprism that consists of 12 great rhombicuboctahedral prisms, 6 octagonal-dodecagonal duoprisms, 8 hexagonal-dodecagonal duoprisms, and 12 square-dodecagonal duoprisms. Each vertex joins 2 great rhombicuboctahedral prisms, 1 square-dodecagonal duoprism, 1 hexagonal-dodecagonal duoprism, and 1 octagonal-dodecagonal duoprism.

This polyteron can be alternated into a hexagonal-snub cubic duoantiprism, although it cannot be made uniform. The dodecagons can also be edge-snubbed to create a snub cubic-hexagonal prismantiprismoid or the great rhombicuboctahedra to create a hexagonal-pyritohedral prismantiprismoid, which are also both nonuniform.

## Vertex coordinates[edit | edit source]

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

## Representations[edit | edit source]

A dodecagonal-great rhombicuboctahedral duoprism has the following Coxeter diagrams:

- x12o x4x3x () (full symmetry)
- x6x x4x3x () (dodecagons as dihexagons)