# Small dodecahemicosahedron

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Small dodecahemicosahedron | |
---|---|

Rank | 3 |

Type | Uniform |

Space | Spherical |

Notation | |

Bowers style acronym | Sidhei |

Coxeter diagram | ()/2 (x5/3o5/2x3*a)/2 |

Elements | |

Faces | 12 pentagrams, 10 hexagons |

Edges | 60 |

Vertices | 30 |

Vertex figure | Bowtie, edge lengths (√5–1)/2 and √3 |

Measures (edge length 1) | |

Circumradius | 1 |

Dihedral angle | |

Number of pieces | 240 |

Level of complexity | 12 |

Related polytopes | |

Army | Id |

Regiment | Did |

Dual | Small dodecahemicosacron |

Conjugate | Great dodecahemicosahedron |

Abstract properties | |

Euler characteristic | –8 |

Topological properties | |

Orientable | No |

Genus | 10 |

Properties | |

Symmetry | H_{3}, order 120 |

Convex | No |

Nature | Tame |

The **small dodecahemicosahedron**, or **sidhei**, is a quasiregular polyhedron and one of 10 uniform hemipolyhedra. It consists of 12 pentagrams and 10 "hemi" hexagons, with two of each joining at a vertex. Its pentagrammic faces are parallel to those of a dodecahedron, and its hemi hexagonal faces are parallel to those of an icosahedron: hence the name "dodecahemicosahedron". The "small" suffix, used for stellations in general, distinguishes it from the great dodecahemicosahedron, which also has this face arrangement.

It is a faceting of the dodecadodecahedron, keeping the original's pentagrams while also using its equatorial hexagons.

## Vertex coordinates[edit | edit source]

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

## External links[edit | edit source]

- Bowers, Jonathan. "Polyhedron Category 3: Quasiregulars" (#28).

- Bowers, Jonathan. "Batch 3: Id, Did, and Gid Facetings" (#2 under did).

- Klitzing, Richard. "sidhei".

- Wikipedia Contributors. "Small dodecahemicosahedron".
- McCooey, David. "Small Dodecahemicosahedron"