# Octagram

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Octagram | |
---|---|

Rank | 2 |

Type | Regular |

Space | Spherical |

Bowers style acronym | Og |

Info | |

Coxeter diagram | x8/3o |

Schläfli symbol | {8/3} |

Symmetry | I2(8), order 16 |

Army | Oc |

Elements | |

Vertex figure | Dyad, length √2–√2 |

Edges | 8 |

Vertices | 8 |

Measures (edge length 1) | |

Circumradius | |

Inradius | |

Area | |

Angle | 45° |

Central density | 3 |

Euler characteristic | 0 |

Number of pieces | 16 |

Level of complexity | 2 |

Related polytopes | |

Dual | Octagram |

Conjugate | Octagon |

Convex core | Octagon |

Properties | |

Convex | No |

Orientable | Yes |

Nature | Tame |

The **octagram**, or **og**, is a non-convex polygon with 8 sides. It's created by stellating the octagon. A regular octagram has equal sides and equal angles.

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

The octagram is the uniform quasitruncation of the square, and as such is the only regular star polygon to regularly appear in non-prismatic uniform polytopes in 5 dimensions and higher.

## Vertex coordinates[edit | edit source]

Coordinates for an octagram of unit edge length, centered at the origin, are all permutations of

## Representations[edit | edit source]

An octagram has the following Coxeter diagrams:

- x8/3o (full symmetry)
- x4/3x (BC2 symmetry)

## External links[edit | edit source]

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

- Klitzing, Richard. "Polygons"
- Wikipedia Contributors. "Octagram".