# Compound of two pentagrams

(Redirected from Stellated decagram)

Compound of two pentagrams | |
---|---|

Rank | 2 |

Type | Regular |

Notation | |

Bowers style acronym | Sadag |

Schläfli symbol | {10/4} |

Elements | |

Components | 2 pentagrams |

Edges | 10 |

Vertices | 10 |

Vertex figure | Dyad, length (√5–1)/2 |

Measures (edge length 1) | |

Circumradius | |

Inradius | |

Area | |

Angle | 36° |

Central density | 4 |

Number of external pieces | 20 |

Level of complexity | 2 |

Related polytopes | |

Army | Dec, edge length |

Dual | Compound of two pentagrams |

Conjugate | Compound of two pentagons |

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 |

The **stellated decagram** or **sadag** is a polygon compound composed of two pentagrams. As such it has 10 edges and 10 vertices.

It is the third stellation of the decagon.

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

## Vertex coordinates[edit | edit source]

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

## Variations[edit | edit source]

The stellated decagram can be varied by changing the angle between the two component pentagrams from the usual 36°. These 2-pentagram compounds generally have a dipentagon as their convex hull and remain uniform,but not regular, with pentagonal symmetry only.

## External links[edit | edit source]

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