# Small dodecahemidodecahedron

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Small dodecahemidodecahedron | |
---|---|

Rank | 3 |

Type | Uniform |

Notation | |

Bowers style acronym | Sidhid |

Coxeter diagram | (x5/4o5x5*a)/2 ()/2 |

Elements | |

Faces | |

Edges | 60 |

Vertices | 30 |

Vertex figure | Bowtie, edge lengths (1+√5)/2 and √(5+√5)/2 |

Measures (edge length 1) | |

Circumradius | |

Dihedral angle | |

Number of external pieces | 72 |

Level of complexity | 4 |

Related polytopes | |

Army | Id |

Regiment | Id |

Dual | Small dodecahemidodecacron |

Conjugate | Great dodecahemidodecahedron |

Abstract & topological properties | |

Flag count | 240 |

Euler characteristic | –12 |

Orientable | No |

Genus | 14 |

Properties | |

Symmetry | H_{3}, order 120 |

Flag orbits | 2 |

Convex | No |

Nature | Tame |

The **small dodecahemidodecahedron**, or **sidhid**, is a quasiregular polyhedron and one of 10 uniform hemipolyhedra. It consists of 12 pentagons and 6 "hemi" decagons, with two of each joining at a vertex.

It can be derived as a rectified petrial icosahedron.

It is a faceting of the icosidodecahedron, keeping the original's pentagons, while also using its equatorial decagons.

## Naming[edit | edit source]

Its pentagonal faces, as well as its hemi decagonal faces, are parallel to those of a dodecahedron, hence the name "dodecahemidodecahedron". The "small" prefix, used for stellations in general, distinguishes it from the great dodecahemidodecahedron, which also has this face arrangement.

## Vertex coordinates[edit | edit source]

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

## External links[edit | edit source]

- Bowers, Jonathan. "Polyhedron Category 3: Quasiregulars" (#25).

- Bowers, Jonathan. "Batch 3: Id, Did, and Gid Facetings" (#3 under id).

- Klitzing, Richard. "sidhid".
- Wikipedia contributors. "Small dodecahemidodecahedron".
- McCooey, David. "Small Dodecahemidodecahedron"