# Small complex icosidodecahedron

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Small complex icosidodecahedron | |
---|---|

Rank | 3 |

Type | Uniform |

Notation | |

Bowers style acronym | Cid |

Coxeter diagram | o5/3o3x5*a () |

Elements | |

Faces | 20 triangles, 12 pentagons, |

Edges | 30 |

Vertices | 12 |

Vertex figure | Complex dipentagon |

Edge figure | Tetrad |

Measures (edge length 1) | |

Circumradius | |

Edge radius | |

Central density | 4 |

Related polytopes | |

Army | Ike |

Regiment | Ike |

Conjugate | Great complex icosidodecahedron |

Convex core | Dodecahedron |

Abstract & topological properties | |

Flag count | 240 |

Properties | |

Symmetry | H_{3}, order 120 |

Flag orbits | 2 |

Convex | No |

The **small complex icosidodecahedron**, or **cid**, is a uniform exotic polyhedroid. It has 12 pentagons and 20 triangles as faces, with 5 of each at a vertex.

It can be seen as a compound of the icosahedron and the great dodecahedron, with their edges coinciding and merging into tetradic edges.

## Vertex coordinates[edit | edit source]

The vertex coordinates of the small complex icosidodecahedron are the same as those of the icosahedron.

## External links[edit | edit source]

- Klitzing, Richard. "cid".
- Wikipedia contributors. "Small complex icosidodecahedron".