Tripod

The tripod is a non-convex semiuniform 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 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.

Valid tripods come in two varieties, the propeller tripod and the non-propeller tripod. The propellor tripod has a density of 1, while the non-propellor tripod has a density of 2.

In vertex figures
The tripod appears as a vertex figure in two uniform polyhedra, namely the ditrigonal dodecadodecahedron and the great ditrigonal icosidodecahedron. In the ditrigonal dodecadodecahedron, it is a propeller tripod and has edge lengths of ($\sqrt{5}$–1)/2 and (1+$\sqrt{5}$)/2. In the great ditrigonal icosidodecahedron, it is a non-propeller tripod and has edge lengths of 1 and (1+$\sqrt{5}$)/2.