# Small rhombidodecahedron

The **small rhombidodecahedron**, or **sird**, is a uniform polyhedron. It consists of 30 squares and 12 decagons. Two squares and two decagons meet at each vertex..

Small rhombidodecahedron | |
---|---|

Rank | 3 |

Type | Uniform |

Notation | |

Bowers style acronym | Sird |

Coxeter diagram | x5/2x5x -12{10/2} |

Elements | |

Faces | 30 squares, 12 decagons |

Edges | 60+60 |

Vertices | 60 |

Vertex figure | Butterfly, edge lengths √2 and √(5+√5)/2 |

Measures (edge length 1) | |

Circumradius | |

Dihedral angles | 4–10 #1: |

4–10 #2: | |

Central density | odd |

Number of external pieces | 150 |

Level of complexity | 10 |

Related polytopes | |

Army | Srid |

Regiment | Srid |

Dual | Small rhombidodecacron |

Conjugate | Great rhombidodecahedron |

Convex core | Dodecahedron |

Abstract & topological properties | |

Flag count | 480 |

Euler characteristic | –18 |

Orientable | No |

Genus | 20 |

Properties | |

Symmetry | H_{3}, order 120 |

Flag orbits | 4 |

Convex | No |

Nature | Tame |

It is a faceting of the small rhombicosidodecahedron, using its 30 squares along with the 12 decagons of the small dodecicosidodecahedron.

The truncated dodecadodecahedron (x5/2x5x) is a degenerate polyhedron with 12 decagons, 30 squares, and 12 doubly-wound pentagons. If those pentagons are blended out, the result is the small rhombidodecahedron.

## Vertex coordinates Edit

Its vertices are the same as those of its regiment colonel, the small rhombicosidodecahedron.

## Representations Edit

A small rhombidodecahedron has representations as two reduced Coxeter diagrams:

- x5/2x5x -12{10/2}
- x3/2x5x -20{6/2}

## External links Edit

- Bowers, Jonathan. "Polyhedron Category 4: Trapeziverts" (#41).

- Klitzing, Richard. "sird".
- Wikipedia contributors. "Small rhombidodecahedron".
- McCooey, David. "small Rhombidodecahedron"