# Small icosihemidodecahedron

Small icosihemidodecahedron | |
---|---|

Rank | 3 |

Type | Uniform |

Notation | |

Bowers style acronym | Seihid |

Coxeter diagram | (x3/2o3x5*a)/2 ()/2 |

Elements | |

Faces | 20 triangles, 6 decagons |

Edges | 60 |

Vertices | 30 |

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

Measures (edge length 1) | |

Circumradius | |

Dihedral angle | |

Number of external pieces | 80 |

Level of complexity | 4 |

Related polytopes | |

Army | Id |

Regiment | Id |

Dual | Small icosihemidodecacron |

Conjugate | Great icosihemidodecahedron |

Abstract & topological properties | |

Flag count | 240 |

Euler characteristic | –4 |

Orientable | No |

Genus | 6 |

Properties | |

Symmetry | H_{3}, order 120 |

Flag orbits | 2 |

Convex | No |

Nature | Tame |

The **small icosihemidodecahedron**, or **seihid**, is a quasiregular polyhedron and one of 10 uniform hemipolyhedra. It consists of 20 equilateral triangles and 6 central decagons, with two of each joining at a vertex.

It can be derived as a rectified petrial dodecahedron.

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

## Name[edit | edit source]

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

## Vertex coordinates[edit | edit source]

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

## External links[edit | edit source]

- Bowers, Jonathan. "Polyhedron Category 3: Quasiregulars" (#26).

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

- Klitzing, Richard. "seihid".
- Wikipedia contributors. "Small icosihemidodecahedron".
- McCooey, David. "Small Icosihemidodecahedron"