# Tripod

Tripod
Rank2
TypeSemi-uniform
Notation
Bowers style acronymTripod
Coxeter diagramx3/2y
Elements
Edges3+3
Vertices6
Measures (edge lengths a , b )
Circumradius${\displaystyle {\sqrt {\frac {a^{2}-ab+b^{2}}{3}}}}$
Area${\displaystyle {\frac {\sqrt {3}}{4}}(4ab-a^{2}-b^{2})}$
Angle60°
Related polytopes
ArmyDit
DualTriambus
ConjugateTripod
Abstract & topological properties
Flag count12
OrientableYes
Properties
SymmetryA2, order 6
Flag orbits2
ConvexNo
NatureTame

The 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 tripod measure 60°.

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.

Another related polygon that has the name "tripod" is the propeller tripod. These two polygons share many of their properties, but while a (non-propeller) tripod has a density of 1, the propeller tripod has a density of 2.

## In vertex figures

The tripod appears as a vertex figure in one uniform polyhedron, namely the great ditrigonal icosidodecahedron. This tripod has edge lengths of 1 and ${\displaystyle {\frac {1+{\sqrt {5}}}{2}}}$.