# Small inverted retrosnub icosicosidodecahedron

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Small inverted retrosnub icosicosidodecahedron | |
---|---|

Rank | 3 |

Type | Uniform |

Space | Spherical |

Notation | |

Bowers style acronym | Sirsid |

Coxeter diagram | s5/2s3/2s3/2*a () |

Elements | |

Faces | 60 triangles, 40 triangles as 20 hexagrams, 12 pentagrams |

Edges | 60+60+60 |

Vertices | 60 |

Vertex figure | Mirror-symmetric hexagon, edge lengths 1, 1, 1, 1, 1, (√5–1)/2 |

Measures (edge length 1) | |

Circumradius | |

Volume | |

Dihedral angles | 5/2–3: |

3–3: | |

Central density | 38 |

Number of external pieces | 3060 |

Level of complexity | 213 |

Related polytopes | |

Army | Semi-uniform Tid, edge lengths (triangles), (between dipentagons) |

Regiment | Sirsid |

Dual | Small hexagrammic hexecontahedron |

Conjugate | Small snub icosicosidodecahedron |

Convex core | Order-6 truncated pentakis dodecahedron |

Abstract & topological properties | |

Flag count | 720 |

Euler characteristic | –8 |

Orientable | Yes |

Properties | |

Symmetry | H_{3}, order 120 |

Convex | No |

Nature | Tame |

The **small inverted retrosnub icosicosidodecahedron**, or **sirsid**, also called the **small retrosnub icosicosidodecahedron**, is a uniform polyhedron. It consists of 60 snub triangles, 40 more triangles that create 20 hexagrams due to pairs lying in the same plane, and 12 pentagrams. Five triangles and one pentagram meet at each vertex.

In terms of level of complexity, this is the most complex uniform polyhedron.

## Vertex coordinates[edit | edit source]

A small inverted retrosnub icosicosidodecahedron of edge length 1 has vertex coordinates given by all even permutations of:

## Representations[edit | edit source]

A small inverted retrosnub icosicosidodecahedron has the following Coxeter diagrams:

- s3/2s3/2s5/2*a
- o5ß3/2ß (as holosnub)

## External links[edit | edit source]

- Bowers, Jonathan. "Polyhedron Category 6: Snubs" (#74).

- Klitzing, Richard. "sirsid".

- Wikipedia Contributors. "Small retrosnub icosicosidodecahedron".
- McCooey, David. "Small Retrosnub Icosicosidodecahedron"