# Small complex rhombicosidodecahedron

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Small complex rhombicosidodecahedron | |
---|---|

Rank | 3 |

Type | Uniform |

Notation | |

Bowers style acronym | Sicdatrid |

Coxeter diagram | x5/2o3x () |

Elements | |

Faces | 20 triangles, 30 squares, 12 pentagrams |

Edges | 60+60 |

Vertices | 20 |

Edge figure | Tetrad |

Measures (edge length 1) | |

Circumradius | |

Central density | 7 |

Related polytopes | |

Army | Doe, edge length |

Regiment | Sidtid |

Conjugate | Great complex rhombicosidodecahedron |

Convex hull | Dodecahedron |

Abstract & topological properties | |

Flag count | 480 |

Euler characteristic | -38 |

Properties | |

Symmetry | H_{3}, order 120 |

Convex | No |

The **small complex rhombicosidodecahedron**, or **sicdatrid**, is a degenerate uniform exotic polyhedroid. It consists of 12 pentagrams, 20 triangles, and 30 squares. 3 pentagrams, 3 triangles, and 6 squares join at each vertex. It can be constructed as a cantellated great icosahedron or great stellated dodecahedron. It can also be seen as a compound of a small ditrigonary icosidodecahedron and a rhombihedron, the compound of 5 cubes, with their edges merging into tetradic edges.

## External links[edit | edit source]

- Klitzing, Richard. "sicdatrid".