# Small dodecicosidodecahedron

The **small dodecicosidodecahedron**, or **saddid**, is a uniform polyhedron. It consists of 20 triangles, 12 pentagons, and 12 decagons. One triangle, one pentagon, and two decagons join at each vertex.

Small dodecicosidodecahedron | |
---|---|

Rank | 3 |

Type | Uniform |

Notation | |

Bowers style acronym | Saddid |

Coxeter diagram | x3/2o5x5*a () |

Elements | |

Faces | 20 triangles, 12 pentagons, 12 decagons |

Edges | 60+60 |

Vertices | 60 |

Vertex figure | Crossed isosceles trapezoid, edge lengths 1, √(5+√5)/2, (1+√5)/2, √(5+√5)/2 |

Measures (edge length 1) | |

Circumradius | |

Volume | |

Dihedral angles | 5–10: |

3–10: | |

Central density | 2 |

Number of external pieces | 152 |

Level of complexity | 9 |

Related polytopes | |

Army | Srid |

Regiment | Srid |

Dual | Small dodecacronic hexecontahedron |

Conjugate | Great dodecicosidodecahedron |

Convex core | Dodecahedron |

Abstract & topological properties | |

Flag count | 480 |

Euler characteristic | –16 |

Orientable | Yes |

Properties | |

Symmetry | H_{3}, order 120 |

Flag orbits | 4 |

Convex | No |

Nature | Tame |

It is a faceting of the small rhombicosidodecahedron, using its 12 pentagons and 20 triangles along with 12 additional decagons.

## Vertex coordinates edit

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

## Representations edit

A small dodecicosidodecahedron has the following Coxeter diagrams:

- x3/2o5x5*a ( )
- x5o3ß ( , as holosnub)

## External links edit

- Bowers, Jonathan. "Polyhedron Category 4: Trapeziverts" (#40).

- Klitzing, Richard. "saddid".
- Wikipedia contributors. "Small dodecicosidodecahedron".
- McCooey, David. "Small Dodecicosidodecahedron"