# Icosidodecahedron atop truncated icosahedron

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Icosidodecahedron atop truncated icosahedron | |
---|---|

Rank | 4 |

Type | Segmentotope |

Notation | |

Bowers style acronym | Idati |

Coxeter diagram | oo5xx3ox&#x |

Elements | |

Cells | 12 pentagonal prisms, 20 triangular cupolas, 1 icosidodecahedron, 1 truncated icosahedron |

Faces | 20+30 triangles, 60 squares, 12+12 pentagons, 20 hexagons |

Edges | 30+60+60+60 |

Vertices | 30+60 |

Vertex figures | 30 wedges, edge lengths 1 (2 base edges and top edges), √2 (sides), and (1+√5)/2 (other base edges) |

60 sphenoids, edge lengths 1 (1), √2 (2), (1+√5)/2 (1), and √3 (2) | |

Measures (edge length 1) | |

Circumradius | |

Hypervolume | |

Dichoral angles | Pip–4–tricu: |

Tricu–3–tricu: | |

Id–5–pip: 162° | |

Id–3–tricu: | |

Ti–6–tricu: | |

Ti–5–pip: 18° | |

Height | |

Central density | 1 |

Related polytopes | |

Army | Idati |

Regiment | Idati |

Dual | Rhombic triacontahedral-pentakis dodecahedral tegmoid |

Conjugate | Great icosidodecahedron atop truncated great icosahedron |

Abstract & topological properties | |

Euler characteristic | 0 |

Orientable | Yes |

Properties | |

Symmetry | H_{3}×I, order 120 |

Convex | Yes |

Nature | Tame |

**Icosidodecahedron atop truncated icosahedron**, or **idati**, is a CRF segmentochoron (designated K-4.158 on Richard Klitzing's list). As the name suggests, it consists of an icosidodecahedron and a truncated icosahedron as bases, connected by 12 pentagonal prisms and 20 triangular cupolas.

It can be obtained as an icosidodecahedron-first cap of the small rhombated hexacosichoron.

## Vertex coordinates[edit | edit source]

The vertices of an icosidodecahedron atop truncated icosahedron segmentochoron of edge length 1 are given by all permutations of the first three coordinates of:

Plus all even permutations of the first three coordinates of:

## External links[edit | edit source]

- Klitzing, Richard. "idati".