# Propeller tripod

Propeller tripod | |
---|---|

Rank | 2 |

Type | Semi-uniform |

Space | Spherical |

Notation | |

Coxeter diagram | x3/2y |

Elements | |

Edges | 3+3 |

Vertices | 6 |

Vertex figure | Dyad |

Measures (edge lengths a, b) | |

Circumradius | |

Area | |

Angle | 60º |

Related polytopes | |

Army | Dit |

Dual | concave triambus |

Abstract & topological properties | |

Orientable | Yes |

Properties | |

Symmetry | A_{2}, order 6 |

Convex | No |

Nature | Tame |

The **propeller tripod** is a non-convex semi-uniform hexagon. As such it has 6 sides that alternate between two edge lengths, with each vertex joining one side of each length. All interior angles of a propeller tripod measure 60º.

If the two edge lengths are equal, then the figure degenerates into something that looks like a double-cover of an equilateral triangle, with pairs of coinciding vertices and edges. However, in any other case the shape is a fully valid polygon.

The propeller tripod can be seen as a variation of the tripod. These two polygons share many of their properties, but while the propeller tripod has a density of 2, a (non-propeller) tripod has a density of 1.

## In vertex figures[edit | edit source]

The propeller tripod appears as a vertex figure in one uniform polyhedron, namely the ditrigonal dodecadodecahedron. This propeller tripod has edge lengths of (√5–1)/2 and (1+√5)/2.

## External links[edit | edit source]

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