# Dodecagram

The **dodecagram** is a star polygon with 12 sides. A regular dodecagram has equal sides and equal angles.

Dodecagram | |
---|---|

Rank | 2 |

Type | Regular |

Space | Spherical |

Notation | |

Bowers style acronym | Dodag |

Coxeter diagram | x12/5o () |

Schläfli symbol | {12/5} |

Elements | |

Edges | 12 |

Vertices | 12 |

Vertex figure | Dyad, length (√6–√2)/2 |

Measures (edge length 1) | |

Circumradius | |

Inradius | |

Area | |

Angle | 30° |

Central density | 5 |

Number of external pieces | 24 |

Level of complexity | 2 |

Related polytopes | |

Army | Dog, edge length |

Dual | Dodecagram |

Conjugate | 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 |

This is the fourth stellation of the dodecagon, and the only one that is not a compound. The only other polygons with a single non-compound stellation are the pentagon, the octagon, and the decagon.

It is the uniform quasitruncation of the hexagon, and as such appears as faces in a handful of uniform Euclidean tilings. It is the largest star polygon known to appear in any non-prismatic spherical or Euclidean uniform polytopes.

## Vertex coordinatesEdit

Coordinates for a dodecagram of unit edge length, centered at the origin, are all permutations of:

## RepresentationsEdit

A dodecagram has the following Coxeter diagrams:

- x12/5o (full symmetry)
- x6/5x ( ) (G
_{2}symmetry)

## External linksEdit

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

- Wikipedia Contributors. "Dodecagram".
- Hartley, Michael. "{12}*24".