# Dodecagonal-cuboctahedral duoprism

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Dodecagonal-cuboctahedral duoprism | |
---|---|

Rank | 5 |

Type | Uniform |

Notation | |

Bowers style acronym | Twaco |

Coxeter diagram | x12o o4x3o () |

Elements | |

Tera | 12 cuboctahedral prisms, 8 triangular-dodecagonal duoprisms, 6 square-dodecagonal duoprisms |

Cells | 96 triangular prisms, 72 squares, 12 cuboctahedra, 24 dodecagonal prisms |

Faces | 96 triangles, 72+288 squares, 12 dodecagons |

Edges | 144+288 |

Vertices | 144 |

Vertex figure | Rectangular scalene, edge lengths 1, √2, 1, √2 (base rectangle), √2+√3 (top), √2 (side edges) |

Measures (edge length 1) | |

Circumradius | |

Hypervolume | |

Diteral angles | Cope–co–cope: 150° |

Titwadip–twip–sitwadip: | |

Titwadip–trip–cope: 90° | |

Sitwadip–cube–cope: 90° | |

Central density | 1 |

Number of external pieces | 26 |

Level of complexity | 20 |

Related polytopes | |

Army | Twaco |

Regiment | Twaco |

Dual | Dodecagonal-rhombic dodecahedral duotegum |

Conjugate | Dodecagrammic-cuboctahedral duoprism |

Abstract & topological properties | |

Flag count | 23040 |

Euler characteristic | 2 |

Orientable | Yes |

Properties | |

Symmetry | B_{3}×I_{2}(12), order 1152 |

Convex | Yes |

Nature | Tame |

The **dodecagonal-cuboctahedral duoprism** or **twaco** is a convex uniform duoprism that consists of 12 cuboctahedral prisms, 6 square-dodecagonal duoprisms, and 8 triangular-dodecagonal duoprisms. Each vertex joins 2 cuboctahedral prisms, 2 triangular-dodecagonal duoprisms, and 2 square-dodecagonal duoprisms.

## Vertex coordinates[edit | edit source]

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

- ,
- ,
- .

## Representations[edit | edit source]

A dodecagonal-cuboctahedral duoprism has the following Coxeter diagrams:

- x12o o4x3o () (full symmetry)
- x6x o4x3o () (dodecagons as dihexagons)
- x12o x3o3x ()
- x6x x3o3x () (dodecagons as dihexagons; cuboctahedron as rhombitetratetrahedron)