# Compound of two great icosahedra

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

Rank | 3 |

Type | Uniform |

Notation | |

Bowers style acronym | Sirsido |

Elements | |

Components | 2 great icosahedra |

Faces | 24 triangles, 16 triangles as 8 hexagrams |

Edges | 12+48 |

Vertices | 24 |

Vertex figure | Regular pentagram, edge length 1 |

Measures (edge length 1) | |

Circumradius | |

Inradius | |

Volume | |

Dihedral angle | |

Central density | 14 |

Number of external pieces | 264 |

Level of complexity | 36 |

Related polytopes | |

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

Regiment | Passipsido |

Dual | Compound of two great stellated dodecahedra |

Conjugate | Compound of two icosahedra |

Convex core | Octatruncated tetrakis hexahedron |

Abstract & topological properties | |

Flag count | 240 |

Orientable | Yes |

Properties | |

Symmetry | B_{3}, order 48 |

Flag orbits | 5 |

Convex | No |

Nature | Tame |

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

It can be constructed from the pentagrammatic snub pseudodisoctahedron by replacing each small stellated dodecahedron with the great icosahedron with which it shares its edges.

## Gallery[edit | edit source]

## Vertex coordinates[edit | edit source]

Its vertices are the same as those of its regiment colonel, the pentagrammatic snub pseudodisoctahedron.

## External links[edit | edit source]

- Bowers, Jonathan. "Polyhedron Category C4: Ikers" (#24).

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