# Dodecagonal-icosahedral duoprism

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Dodecagonal-icosahedral duoprism | |
---|---|

Rank | 5 |

Type | Uniform |

Notation | |

Bowers style acronym | Twike |

Coxeter diagram | x12o o5o3x () |

Elements | |

Tera | 20 triangular-dodecagonal duoprisms, 12 icosahedral prisms |

Cells | 240 triangular prisms, 30 dodecagonal prisms, 12 icosahedra |

Faces | 240 triangles, 360 squares, 12 dodecagons |

Edges | 144+360 |

Vertices | 144 |

Vertex figure | Pentagonal scalene, edge lengths 1 (base pentagon), √2+√3 (top), √2 (sides) |

Measures (edge length 1) | |

Circumradius | |

Hypervolume | |

Diteral angles | Ipe–ike–ipe: 150° |

Titwadip–twip–titwadip: | |

Titwadip–trip–ipe: 90° | |

Central density | 1 |

Related polytopes | |

Army | Twike |

Regiment | Twike |

Dual | Dodecagonal-dodecahedral duotegum |

Conjugates | Dodecagrammic-icosahedral duoprism, Dodecagonal-great icosahedral duoprism, Dodecagrammic-great icosahedral duoprism |

Abstract & topological properties | |

Euler characteristic | 2 |

Orientable | Yes |

Properties | |

Symmetry | H_{3}×I2(12), order 2880 |

Convex | Yes |

Nature | Tame |

The **dodecagonal-icosahedral duoprism** or **twike** is a convex uniform duoprism that consists of 12 icosahedral prisms and 20 triangular-dodecagonal duoprisms. Each vertex joins 2 icosahedral prisms and 5 triangular-dodecahedral duoprisms.

## Vertex coordinates[edit | edit source]

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

## Representations[edit | edit source]

A dodecagonal-icosahedral duoprism has the following Coxeter diagrams:

- x12o o5o3x () (full symmetry)
- x6x o5o3x () (dodecagons as dihexagons)