# Propeller tripod

Propeller tripod
Rank2
TypeSemi-uniform
Notation
Coxeter diagramx3/2y
Elements
Edges3+3
Vertices6
Measures (edge lengths a, b)
Circumradius${\displaystyle {\sqrt {\frac {a^{2}-ab+b^{2}}{3}}}}$
Area${\displaystyle {\frac {\sqrt {3}}{4}}(4ab-a^{2}-b^{2})}$
Angle60º
Related polytopes
ArmyDit
Dualconcave triambus
Abstract & topological properties
Flag count12
OrientableYes
Properties
SymmetryA2, order 6
Flag orbits2
ConvexNo
NatureTame

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 (5–1)/2 and (1+5)/2.