# Icosidodecahedral prism

Icosidodecahedral prism | |
---|---|

Rank | 4 |

Type | Uniform |

Space | Spherical |

Notation | |

Bowers style acronym | Iddip |

Coxeter diagram | x o5x3o () |

Elements | |

Cells | 20 triangular prisms, 12 pentagonal prisms, 2 icosidodecahedra |

Faces | 40 triangles, 60 squares, 24 pentagons |

Edges | 30+120 |

Vertices | 60 |

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

Measures (edge length 1) | |

Circumradius | |

Hypervolume | |

Dichoral angles | Trip–4–pip: |

Id–3–trip: 90° | |

Id–5–pip: 90° | |

Height | 1 |

Central density | 1 |

Number of external pieces | 34 |

Level of complexity | 8 |

Related polytopes | |

Army | Iddip |

Regiment | Iddip |

Dual | Rhombic triacontahedral tegum |

Conjugate | Great icosidodecahedral prism |

Abstract & topological properties | |

Flag count | 1920 |

Euler characteristic | 0 |

Orientable | Yes |

Properties | |

Symmetry | H_{3}×A_{1}, order 240 |

Convex | Yes |

Nature | Tame |

The **icosidodecahedral prism** or **iddip**, is a prismatic uniform polychoron that consists of 2 icosidodecahedra, 12 pentagonal prisms, and 20 triangular prisms. Each vertex joins 1 icosidodecahedron, 2 pentagonal prisms, and 2 triangular prisms. It is a prism based on the icosidodecahedron. As such it is also a convex segmentochoron (designated K-4.90 on Richard Klitzing's list).

## Gallery[edit | edit source]

Card with cell counts, verf, and cross-sections

Segmentochoron display, id atop id

## Vertex coordinates[edit | edit source]

The vertices of an icosidodecahedral prism of edge length 1 are given by all permutations and sign changes of the first three coordinates of:

along with all even permutations and all sign changes of the first three coordinates of:

## Representations[edit | edit source]

An icosidodecahedral prism has the following Coxeter diagrams:

- x o5x3o (full symmetry)
- oo5xx3oo&#x (bases seen separately)
- xxxxx xoxfo5ofxox&#xt (H
_{2}×A_{1}axial, pentagonal prism-first)

## Related polychora[edit | edit source]

The regiment of the icosidodecahedral prism also includes the small icosihemidodecahedral prism and small dodecahemidodecahedral prism.

## External links[edit | edit source]

- Bowers, Jonathan. "Category 19: Prisms" (#911).

- Klitzing, Richard. "Iddip".

- Wikipedia Contributors. "Icosidodecahedral prism".