# Small dodecicosidodecahedral prism

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

Rank | 4 |

Type | Uniform |

Space | Spherical |

Notation | |

Bowers style acronym | Saddiddip |

Coxeter diagram | x x3/2o5x5*b () |

Elements | |

Cells | 20 triangular prisms, 12 pentagonal prisms, 12 decagonal prisms, 2 small dodecicosidodecahedra |

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

Edges | 60+120+120 |

Vertices | 120 |

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

Measures (edge length 1) | |

Circumradius | |

Hypervolume | |

Dichoral angles | Pip–4–dip: |

Saddid–5–pip: 90° | |

Saddid–3–trip: 90° | |

Saddid–10–dip: 90° | |

Trip–4–dip: | |

Height | 1 |

Central density | 2 |

Number of pieces | 194 |

Related polytopes | |

Army | Sriddip |

Regiment | Sriddip |

Dual | Small dodecacronic hexecontahedral tegum |

Conjugate | Great dodecicosidodecahedral prism |

Abstract properties | |

Euler characteristic | –18 |

Topological properties | |

Orientable | Yes |

Properties | |

Symmetry | H_{3}×A_{1}, order 240 |

Convex | No |

Nature | Tame |

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

## Vertex coordinates[edit | edit source]

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

## External links[edit | edit source]

- Bowers, Jonathan. "Category 19: Prisms" (#927).

- Klitzing, Richard. "saddiddip".