# Icosidodecatruncated icosidodecahedral prism

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Icosidodecatruncated icosidodecahedral prism | |
---|---|

Rank | 4 |

Type | Uniform |

Space | Spherical |

Notation | |

Bowers style acronym | Idtiddip |

Coxeter diagram | x x5/3x3x5*b () |

Elements | |

Cells | 20 hexagonal prisms, 12 decagonal prisms, 12 decagrammic prisms, 2 icosidodecatruncated icosidodecahedra |

Faces | 60+60+60 squares, 40 hexagons, 24 decagons, 24 decagrams |

Edges | 120+120+120+120 |

Vertices | 240 |

Vertex figure | Irregular tetrahedron, edge lengths √3, √(5+√5)/2, √(5–√5)/2 (base), √2 (legs) |

Measures (edge length 1) | |

Circumradius | |

Hypervolume | 80 |

Dichoral angles | Hip–4–stiddip: |

Dip–4–stiddip: | |

Hip–4–dip: | |

Idtid–10/3–stiddip: 90° | |

Idtid–10–dip: 90° | |

Idtid–6–hip: 90° | |

Height | 1 |

Central density | 4 |

Number of pieces | 154 |

Related polytopes | |

Army | Semi-uniform Griddip |

Regiment | Idtiddip |

Dual | Tridyakis icosahedral tegum |

Conjugate | Icosidodecatruncated icosidodecahedral prism |

Abstract properties | |

Euler characteristic | –18 |

Topological properties | |

Orientable | Yes |

Properties | |

Symmetry | H_{3}×A_{1}, order 240 |

Convex | No |

Nature | Tame |

The **icosidodecatruncated icosidodecahedral prism** or **idtiddip**, is a prismatic uniform polychoron that consists of 2 icosidodecatruncated icosidodecahedra, 12 decagrammic prisms, 12 decagonal prisms, and 20 hexagonal prisms. Each vertex joins one of each type of cell. as the name suggests, it is a prism based on the icosidodecatruncated icosidodecahedron.

## Vertex coordinates[edit | edit source]

The vertices of an icosidodecatruncated icosidodecahedral prism of edge length 1 are given by all even permutations of the first three coordinates of:

## External links[edit | edit source]

- Bowers, Jonathan. "Category 19: Prisms" (#950).

- Klitzing, Richard. "idtiddip".