# Dodecagonal-snub cubic duoprism

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Dodecagonal-snub cubic duoprism | |
---|---|

Rank | 5 |

Type | Uniform |

Notation | |

Bowers style acronym | Twasnic |

Coxeter diagram | x12o s4s3s () |

Elements | |

Tera | 8+24 triangular-dodecagonal duoprisms, 6 square-dodecagonal duoprisms, 12 snub cubic prisms |

Cells | 96+288 triangular prisms, 72 cubes, 12+24+24 dodecagonal prisms, 12 snub cubes |

Faces | 96+288 triangles, 72+144+288+288 squares, 24 dodecagons |

Edges | 144+288+288+288 |

Vertices | 288 |

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

Measures (edge length 1) | |

Circumradius | ≈ 2.35321 |

Hypervolume | ≈ 88.33182 |

Diteral angles | Titwadip–twip–titwadip: ≈ 153.23459° |

Sniccup–snic–sniccup: 150° | |

Titwadip–twip–sitwadip: ≈ 142.98343° | |

Titwadip–trip–sniccup: 90° | |

Sitwadip–cube–sniccup: 90° | |

Central density | 1 |

Number of external pieces | 50 |

Level of complexity | 50 |

Related polytopes | |

Army | Twasnic |

Regiment | Twasnic |

Dual | Dodecagonal-pentagonal icositetrahedral duotegum |

Conjugate | Dodecagrammic-snub cubic duoprism |

Abstract & topological properties | |

Euler characteristic | 2 |

Orientable | Yes |

Properties | |

Symmetry | B_{3}+×I2(12), order 576 |

Convex | Yes |

Nature | Tame |

The **dodecagonal-snub cubic duoprism** or **twasnic** is a convex uniform duoprism that consists of 12 snub cubic prisms, 6 square-dodecagonal duoprisms, and 32 triangular-dodecagonal duoprisms of two kinds. Each vertex joins 2 snub cubic prisms, 4 triangular-dodecagonal duoprisms, and 1 square-dodecagonal duoprism.

## Vertex coordinates[edit | edit source]

The vertices of a dodecagonal-snub cubic duoprism of edge length 1 are given by by all even permutations with an even number of sign changes, plus all odd permutations with an odd amount of sign changes, of the last three coordinates of:

where