# Small dodecahemidodecahedral prism

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Small dodecahemidodecahedral prism | |
---|---|

Rank | 4 |

Type | Uniform |

Notation | |

Bowers style acronym | Sidhiddip |

Coxeter diagram | /2 ((x x5/4o5x5*b)/2) |

Elements | |

Cells | 12 pentagonal prisms, 6 decagonal prisms, 2 small dodecahemidodecahedra |

Faces | 60 squares, 24 pentagons, 12 decagons |

Edges | 30+120 |

Vertices | 60 |

Vertex figure | Bowtie pyramid, edge lengths (1+√5)/2, √(5+√5)/2 (base), √2 (legs) |

Measures (edge length 1) | |

Circumradius | |

Dichoral angles | Sidhid–5–pip: 90° |

Sidhid–10–dip: 90° | |

Pip–4–dip: | |

Height | 1 |

Number of external pieces | 96 |

Related polytopes | |

Army | Iddip |

Regiment | Iddip |

Dual | Small dodecahemidodecacronic tegum |

Conjugate | Great dodecahemidodecahedral prism |

Abstract & topological properties | |

Euler characteristic | –14 |

Orientable | No |

Properties | |

Symmetry | H_{3}×A_{1}, order 240 |

Convex | No |

Nature | Tame |

The **small dodecahemidodecahedral prism** or **sidhiddip**, is a prismatic uniform polychoron that consists of 2 small dodecahemidodecahedra, 12 pentagonal prisms, and 6 decagonal prisms. Each vertex joins 1 small dodecahemidodecahedron, 2 pentagonal prisms, and 2 decagonal prisms. As the name suggests, it is a prism based on the small dodecahemidodecahedron.

## Vertex coordinates[edit | edit source]

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

## External links[edit | edit source]

- Bowers, Jonathan. "Category 19: Prisms" (#912).