# Compound of twenty octahedra with rotational freedom

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Compound of twenty octahedra with rotational freedom | |
---|---|

Rank | 3 |

Type | Uniform |

Notation | |

Bowers style acronym | Addasi |

Elements | |

Components | 20 octahedra |

Faces | 40+120 triangles |

Edges | 120+120 |

Vertices | 120 |

Vertex figure | Square, edge length 1 |

Measures (edge length 1) | |

Circumradius | |

Inradius | |

Volume | |

Dihedral angle | |

Central density | 20 |

Related polytopes | |

Army | Semi-uniform Grid |

Regiment | Addasi |

Dual | Compound of twenty cubes with rotational freedom |

Conjugate | Compound of twenty octahedra with rotational freedom |

Abstract & topological properties | |

Schläfli type | {3,4} |

Orientable | Yes |

Properties | |

Symmetry | H_{3}, order 120 |

Convex | No |

Nature | Tame |

The **altered disnub icosahedron**, **addasi**, or **compound of twenty octahedra with rotational freedom** is a uniform polyhedron compound. It consists of 40+120 triangles, with 4 triangles joining at each vertex.

This compound has rotational freedom, represented by an angle θ. The 20 octahedra can each be thought of as triangular antiprisms, and we rotate them in pairs in opposite directions. This compound goes through the following phases as θ increases:

- θ = 0°: Double-cover of the snub icosahedron
- 0° < θ < : General phase sometimes known as the
**outer disnub icosahedron**or**oddasi** - θ = : Vertices coincide by pairs to form the disnub icosahedron
- < θ < : General phase sometimes known as the
**inner disnub icosahedron**or**iddasi** - θ = : Octahedra coincide by four, forming a quadruple-cover of the small icosicosahedron
- < θ < 60°: General phase known as the
**great disnub icosahedron**or**giddasi** - θ = 60°: Double-cover of the great snub icosahedron

## Vertex coordinates[edit | edit source]

The vertices of an altered disnub icosahedron of edge length 1 and rotation angle θ are given by all even permutations of:

## External links[edit | edit source]

- Bowers, Jonathan. "Polyhedron Category C9: Octahedral Continuums" (#63, 64, 65).

- Klitzing, Richard. "addasi".
- Wikipedia contributors. "Compound of twenty octahedra with rotational freedom".