# Rhombidodecadodecahedral prism

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Rhombidodecadodecahedral prism | |
---|---|

Rank | 4 |

Type | Uniform |

Space | Spherical |

Notation | |

Bowers style acronym | Radiddip |

Coxeter diagram | x x5/2o5x () |

Elements | |

Cells | 30 cubes, 12 pentagonal prisms, 12 pentagrammic prisms, 2 rhombidodecadodecahedra |

Faces | 60+60+60 squares, 24 pentagons, 24 pentagrams |

Edges | 60+120+120 |

Vertices | 120 |

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

Measures (edge length 1) | |

Circumradius | |

Hypervolume | |

Dichoral angles | Cube–4–stip: |

Cube–4–pip: | |

Raded–5/2–stip: 90° | |

Raded–5–pip: 90° | |

Raded–4–cube: 90° | |

Height | 1 |

Central density | 3 |

Related polytopes | |

Army | Semi-uniform Tipe |

Regiment | Radiddip |

Dual | Medial deltoidal hexecontahedral tegum |

Conjugate | Rhombidodecadodecahedral prism |

Abstract properties | |

Euler characteristic | –8 |

Topological properties | |

Orientable | Yes |

Properties | |

Symmetry | H_{3}×A_{1}, order 240 |

Convex | No |

Nature | Tame |

The **rhombidodecadodecahedral prism** or **radiddip** is a prismatic uniform polychoron that consists of 2 rhombidodecadodecahedra, 12 pentagonal prisms, 12 pentagrammic prisms, and 30 cubes. Each vertex joins 1 rhombidodecadodecahedron, 1 pentagonal prism, 1 pentagrammic prism, and 2 cubes. As the name suggests, it is a prism based on the rhombidodecadodecahedron.

The rhombidodecadodecahedral prism can be vertex-inscribed into the ditetrahedronary dishecatonicosachoron.

## Vertex coordinates[edit | edit source]

The vertices of a rhombidodecadodecahedral prism of edge length 1 are given by all permutations of the first three coordinates of:

along with all even permutations of the first three coordinates of:

## External links[edit | edit source]

- Bowers, Jonathan. "Category 19: Prisms" (#929).

- Klitzing, Richard. "radiddip".