# Decagram

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Decagram | |
---|---|

Rank | 2 |

Type | Regular |

Space | Spherical |

Bowers style acronym | Dag |

Info | |

Coxeter diagram | x10/3o |

Schläfli symbol | {10/3} |

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

Army | Dec |

Elements | |

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

Edges | 10 |

Vertices | 10 |

Measures (edge length 1) | |

Circumradius | |

Inradius | |

Area | |

Angle | 72° |

Central density | 3 |

Euler characteristic | 0 |

Number of pieces | 20 |

Level of complexity | 2 |

Related polytopes | |

Dual | Decagram |

Conjugate | Decagon |

Convex core | Decagon |

Properties | |

Convex | No |

Orientable | Yes |

Nature | Tame |

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

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 coordinates[edit | edit source]

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

## Representations[edit | edit source]

A decagram has the following Coxeter diagrams:

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

## External links[edit | edit source]

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

- Klitzing, Richard. "Polygons"
- Wikipedia Contributors. "Decagram (geometry)".