# Small ditrigonal dodecicosidodecahedral prism

Jump to navigation
Jump to search

Small ditrigonal dodecicosidodecahedral prism | |
---|---|

Rank | 4 |

Type | Uniform |

Notation | |

Bowers style acronym | Sidditdiddip |

Coxeter diagram | x x5/3o3x5*b () |

Elements | |

Cells | 20 triangular prisms, 12 pentagrammic prisms, 12 decagonal prisms, 2 small ditrigonal dodecicosidodecahedra |

Faces | 40 triangles, 60+60 squares, 24 pentagrams, 24 decagons |

Edges | 60+120+120 |

Vertices | 120 |

Vertex figure | Crossed isosceles trapezoidal pyramid, edge lengths 1, √(5+√5)/2, (√5–1)/2, √(5+√5)/2 (base), √2 (legs) |

Measures (edge length 1) | |

Circumradius | |

Hypervolume | |

Dichoral angles | Trip–4–stiddip: |

Sidditdid–5/2–stip: 90° | |

Sidditdid–3–trip: 90° | |

Sidditdid–10–dip: 90° | |

Stip–4–dip: | |

Height | 1 |

Central density | 4 |

Number of external pieces | 238 |

Related polytopes | |

Army | Semi-uniform Sriddip |

Regiment | Siidip |

Dual | Small ditrigonal dodecacronic hexecontahedral tegum |

Conjugate | Great ditrigonal dodecicosidodecahedral prism |

Abstract & topological properties | |

Euler characteristic | –18 |

Orientable | Yes |

Properties | |

Symmetry | H3×A1, order 240 |

Convex | No |

Nature | Tame |

The **small ditrigonal dodecicosidodecahedral prism** or **sidditdiddip** is a prismatic uniform polychoron that consists of 2 small ditrigonal dodecicosidodecahedra, 12 pentagrammic prisms, 20 triangular prisms, and 12 decagonal prisms. Each vertex joins 1 small ditrigonal dodecicosidodecahedron, 1 pentagrammic prism, 1 triangular prism, and 2 decagonal prisms. As the name suggests, it is a prism based on the small ditrigonal dodecicosidodecahedron.

## Vertex coordinates[edit | edit source]

Its vertices are the same as those of its regiment colonel, the small icosicosidodecahedral prism.

## External links[edit | edit source]

- Bowers, Jonathan. "Category 19: Prisms" (#942).

- Klitzing, Richard. "sidditdiddip".