# Stellated octagon

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Stellated octagon | |
---|---|

Rank | 2 |

Type | Regular |

Space | Spherical |

Notation | |

Bowers style acronym | Soc |

Coxeter diagram | xo4ox |

Schläfli symbol | {8/2} |

Elements | |

Components | 2 squares |

Edges | 8 |

Vertices | 8 |

Vertex figure | Dyad, length √2 |

Measures (edge length 1) | |

Circumradius | |

Inradius | |

Area | 2 |

Angle | 90° |

Central density | 2 |

Number of external pieces | 16 |

Level of complexity | 2 |

Related polytopes | |

Army | Oc, edge length |

Dual | Stellated octagon |

Conjugate | Stellated octagon |

Convex core | Octagon |

Abstract & topological properties | |

Flag count | 16 |

Euler characteristic | 0 |

Orientable | Yes |

Properties | |

Symmetry | I_{2}(8), order 16 |

Convex | No |

Nature | Tame |

The **stellated octagon**, or **soc** is a polygon compound composed of two squares. As such it has 8 edges and 8 vertices.

It is the first stellation of the octagon.

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

## Vertex coordinates[edit | edit source]

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

## Variations[edit | edit source]

The stellated octagon can be varied by changing the angle between the two component squares from the usual 45°. These 2-square compounds generally have a ditetragon as their convex hull and remain uniform, but not regular, with square symmetry only.

## External links[edit | edit source]

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