# Compound of two icosahedra

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Compound of two icosahedra | |
---|---|

Rank | 3 |

Type | Uniform |

Notation | |

Bowers style acronym | Siddo |

Coxeter diagram | o4ß3ß () |

Elements | |

Components | 2 icosahedra |

Faces | 24 triangles, 16 triangles as 8 hexagrams |

Edges | 12+48 |

Vertices | 24 |

Vertex figure | Regular pentagon, edge length 1 |

Measures (edge length 1) | |

Circumradius | |

Inradius | |

Volume | |

Dihedral angle | |

Central density | 2 |

Number of external pieces | 80 |

Level of complexity | 13 |

Related polytopes | |

Army | Semi-uniform Toe, edge lengths (squares), (between ditrigons) |

Regiment | Siddo |

Dual | Compound of two dodecahedra |

Conjugate | Compound of two great icosahedra |

Convex core | Order-6 truncated tetrakis hexahedron |

Abstract & topological properties | |

Flag count | 240 |

Schläfli type | {3,5} |

Orientable | Yes |

Properties | |

Symmetry | B_{3}, order 48 |

Flag orbits | 5 |

Convex | No |

Nature | Tame |

The **snub disoctahedron**, **siddo**, or **compound of two icosahedra** is a uniform polyhedron compound. It consists of 40 triangles (8 pairs of which form hexagrams due to falling in the same plane), with five faces joining at a vertex.

The icosahedra have pyritohedral symmetry, and can be seen as two forms of alternation of the semi-uniform truncated octahedron that is its convex hull.

Its quotient prismatic equivalent is the pyritohedral icosahedral antiprism, which is four-dimensional.

## Gallery[edit | edit source]

## Vertex coordinates[edit | edit source]

The vertices of a snub disoctahedron of edge length 1 can be given by all permutations of:

## External links[edit | edit source]

- Bowers, Jonathan. "Polyhedron Category C4: Ikers" (#21).

- Klitzing, Richard. "siddo".
- Wikipedia contributors. "Compound of two icosahedra".