Propeller tripod

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
The propeller tripod appears as a vertex figure in one uniform polyhedron, namely the ditrigonal dodecadodecahedron. This propeller tripod has edge lengths of ($\sqrt{3}$–1)/2 and (1+$\sqrt{(a^{2}–ab+b^{2})/3}$)/2.