# Small dodecicosahedron

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Small dodecicosahedron | |
---|---|

Rank | 3 |

Type | Uniform |

Space | Spherical |

Notation | |

Bowers style acronym | Siddy |

Elements | |

Faces | 20 hexagons, 12 decagons |

Edges | 60+60 |

Vertices | 60 |

Vertex figure | Butterfly, edge lengths √3 and √(5+√5)/2 |

Measures (edge length 1) | |

Circumradius | |

Dihedral angles | 6–10 #1: |

6–10 #2: | |

Central density | even |

Number of external pieces | 320 |

Level of complexity | 18 |

Related polytopes | |

Army | Semi-uniform Srid, edge lengths (pentagons), 1 (triangles) |

Regiment | Siid |

Dual | Small dodecicosacron |

Conjugate | Great dodecicosahedron |

Convex core | Dodecahedron |

Abstract & topological properties | |

Flag count | 480 |

Euler characteristic | –28 |

Orientable | No |

Genus | 30 |

Properties | |

Symmetry | H_{3}, order 120 |

Convex | No |

Nature | Tame |

The **small dodecicosahedron**, or **siddy**, is a uniform polyhedron. It consists of 20 hexagons and 12 decagons. Two hexagons and two decagons meet at each vertex..

It is a faceting of the small icosicosidodecahedron, using its 20 hexagons along with the 12 decagons of the small ditrigonal dodecicosidodecahedron.

## Vertex coordinates[edit | edit source]

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

## External links[edit | edit source]

- Bowers, Jonathan. "Polyhedron Category 4: Trapeziverts" (#53).

- Klitzing, Richard. "siddy".

- Wikipedia Contributors. "Small dodecicosahedron".
- McCooey, David. "Small Dodecicosahedron"