# Truncated icosahedral prism

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Truncated icosahedral prism | |
---|---|

Rank | 4 |

Type | Uniform |

Space | Spherical |

Notation | |

Bowers style acronym | Tipe |

Coxeter diagram | x o5x3x () |

Elements | |

Cells | 12 pentagonal prisms, 20 hexagonal prisms, 2 truncated icosahedra |

Faces | 30+60 squares, 24 pentagons, 40 hexagons |

Edges | 60+60+120 |

Vertices | 120 |

Vertex figure | Sphenoid, edge lengths (1+√5)/2, √3, √3 (base), √2 (legs) |

Measures (edge length 1) | |

Circumradius | |

Hypervolume | |

Dichoral angles | Pip–4–hip: |

Hip–4–hip: | |

Ti–5–pip: 90° | |

Ti–6–hip: 90° | |

Height | 1 |

Central density | 1 |

Number of pieces | 34 |

Level of complexity | 12 |

Related polytopes | |

Army | Tipe |

Regiment | Tipe |

Dual | Pentakis dodecahedral tegum |

Conjugate | Truncated great icosahedral prism |

Abstract properties | |

Flag count | 2880 |

Euler characteristic | 0 |

Topological properties | |

Orientable | Yes |

Properties | |

Symmetry | H_{3}×A_{1}, order 240 |

Convex | Yes |

Nature | Tame |

The **truncated icosahedral prism** or **tipe** is a prismatic uniform polychoron that consists of 2 truncated icosahedra, 12 pentagonal prisms, and 20 hexagonal prisms. Each vertex joins 1 truncated icosahedron, 1 pentagonal prism, and 2 hexagonal prisms. It is a prism based on the truncated icosahedron. As such it is also a CRF segmentochoron (designated K-4.127 on Richard Klitzing's list).

## Gallery[edit | edit source]

Segmentochoron display, ti atop ti

## Vertex coordinates[edit | edit source]

Coordinates for the vertices of a truncated icosahedral prism of edge length 1 are given by all even permutations of the first three coordinates of:

## Representations[edit | edit source]

A truncated icosahedral prism has the following Coxeter diagrams:

- x o5x3x (full symmetry)
- oo5xx3xx&#x (bases considered separately)

## External links[edit | edit source]

- Bowers, Jonathan. "Category 19: Prisms" (#902).

- Klitzing, Richard. "Tipe".

- Wikipedia Contributors. "Truncated icosahedral prism".