# Stellated dodecagon

The **stellated dodecagon**, or **sedog**, is a polygon compound composed of two hexagons. As such it has 12 edges and 12 vertices.

Stellated dodecagon | |
---|---|

Rank | 2 |

Type | Regular |

Space | Spherical |

Notation | |

Bowers style acronym | Sedog |

Schläfli symbol | {12/2} |

Elements | |

Components | 2 hexagons |

Edges | 12 |

Vertices | 12 |

Vertex figure | Dyad, length √3 |

Measures (edge length 1) | |

Circumradius | 1 |

Inradius | |

Area | |

Angle | 120° |

Central density | 2 |

Number of external pieces | 24 |

Level of complexity | 2 |

Related polytopes | |

Army | Dog, edge length |

Dual | Stellated dodecagon |

Conjugate | Stellated dodecagon |

Convex core | Dodecagon |

Abstract & topological properties | |

Flag count | 24 |

Euler characteristic | 0 |

Orientable | Yes |

Properties | |

Symmetry | I_{2}(12), order 24 |

Convex | No |

Nature | Tame |

As the name suggests, it is the first stellation of the dodecagon.

Its quotient prismatic equivalent is the hexagonal antiprism, which is three-dimensional.

## Vertex coordinatesEdit

Coordinates for the vertices of a stellated dodecagon of edge length 1 centered at the origin are given by:

## VariationsEdit

The stellated dodecagon can be varied by changing the angle between the two component hexagons from the usual 30°. These 2-hexagon compounds generally have a dihexagon as their convex hull and remain uniform, but not regular, with hexagonal symmetry only.

## External linksEdit

- Bowers, Jonathan. "Regular Polygons and Other Two Dimensional Shapes".