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 | A2, 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".