Tripod

Tripod
Rank	2
Type	Semi-uniform
Space	Spherical
Notation
Bowers style acronym	Tripod
Coxeter diagram	x3/2y
Elements
Edges	3+3
Vertices	6
Vertex figure	Dyad
Measures (edge lengths a, b)
Circumradius	$\sqrt{\frac{a^2-ab+b^2}{3}}$
Area	$\frac{\sqrt3}{4}(4ab-a^2-b^2)$
Angle	60°
Related polytopes
Army	Dit
Dual	Triambus
Conjugate	Tripod
Abstract & topological properties
Orientable	Yes
Properties
Symmetry	A2, order 6
Convex	No
Nature	Tame

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 (1+√5)/2.

External links

• Bowers, Jonathan. "Regular Polygons and Other Two Dimensional Shapes".