# Decagram

The **decagram** is a star polygon with 10 sides. A regular decagram has equal sides and equal angles.

Decagram | |
---|---|

Rank | 2 |

Type | Regular |

Space | Spherical |

Notation | |

Bowers style acronym | Dag |

Coxeter diagram | x10/3o () |

Schläfli symbol | {10/3} |

Elements | |

Edges | 10 |

Vertices | 10 |

Vertex figure | Dyad, length √(5–√5)/2 |

Measures (edge length 1) | |

Circumradius | |

Inradius | |

Area | |

Angle | 72° |

Central density | 3 |

Number of external pieces | 20 |

Level of complexity | 2 |

Related polytopes | |

Army | Dec, edge length |

Dual | Decagram |

Conjugate | Decagon |

Convex core | Decagon |

Abstract & topological properties | |

Flag count | 20 |

Euler characteristic | 0 |

Orientable | Yes |

Properties | |

Symmetry | I_{2}(10), order 20 |

Convex | No |

Nature | Tame |

It is the second stellation of the decagon, 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 dodecagon.

It is the uniform quasitruncation of the pentagram, and as such appears frequently in uniform polyhedra and polychora. It is the largest uniform star polygon to appear in a non-prismatic uniform polytope in 3 or 4 dimensions.

## Vertex coordinatesEdit

Coordinates for a decagram of unit edge length, centered at the origin, are:

## RepresentationsEdit

A decagram has the following Coxeter diagrams:

- x10/3o (full symmetry)
- x5/3x (H
_{2}symmetry)

## External linksEdit

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

- Klitzing, Richard. "Polygons"
- Wikipedia Contributors. "Decagram (geometry)".
- Hartley, Michael. "{10}*20".