# Hexagram

A **hexagram** is any six-sided polygon, unicursal or compound, that has a density of two. The unqualified usage of "hexagram" usually refers only to the compound figure featured here, though the duals of the great ditrigonal icosidodecahedron and the small retrosnub icosicosidodecahedron also involve other hexagrammic faces.

Hexagram | |
---|---|

Rank | 2 |

Type | Regular |

Space | Spherical |

Notation | |

Bowers style acronym | Shig |

Coxeter diagram | xo3ox |

Schläfli symbol | {6/2} |

Elements | |

Components | 2 triangles |

Edges | 6 |

Vertices | 6 |

Vertex figure | Dyad, length 1 |

Measures (edge length 1) | |

Circumradius | |

Inradius | |

Area | |

Angle | 60° |

Central density | 2 |

Number of external pieces | 12 |

Level of complexity | 2 |

Related polytopes | |

Army | Hig, edge length |

Dual | Hexagram |

Conjugate | Hexagram |

Convex core | Hexagon |

Abstract & topological properties | |

Flag count | 12 |

Euler characteristic | 0 |

Orientable | Yes |

Properties | |

Symmetry | G_{2}, order 12 |

Convex | No |

Nature | Tame |

The **regular hexagram**, or **shig**, also called the **stellated hexagon**, is the simplest possible polygon compound, being the compound of two triangles. As such it has 6 edges and 6 vertices. If the components are equilateral triangles, the compound will be regular.

It is the only stellation of the regular hexagon, which is the polygon with most sides to have no stellations aside from compounds.

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

## Vertex coordinatesEdit

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

## VariationsEdit

The regular hexagram can be varied by changing the angle between the two component triangles from the usual 60°. These 2-triangle compounds generally have a ditrigon as their convex hull and remain uniform, but not regular, with triangular symmetry only.

## External linksEdit

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

- Nan Ma. "Hexagram {6/2}".

- Wikipedia Contributors. "Hexagram".