Ditrigon

Ditrigon
Rank	2
Type	Semi-uniform
Space	Spherical
Notation
Bowers style acronym	Dit
Coxeter diagram	x3y
Elements
Edges	3+3
Vertices	6
Vertex figure	Dyad
Measures (edge lengths a, b)
Circumradius	$\sqrt{\frac{a^2+ab+b^2}{3}}$
Area	$\frac{\sqrt3}{4}(a^2+4ab+b^2)$
Angle	120°
Central density	1
Related polytopes
Army	Dit
Dual	Triambus
Conjugate	Ditrigon
Abstract properties
Flag count	6+6
Net count	1
Euler characteristic	0
Topological properties
Orientable	Yes
Properties
Symmetry	A2, order 6
Convex	Yes
Nature	Tame

The ditrigon is a 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 ditrigon measure 120°. If the side lengths are equal, the result is the regular hexagon.

Vertex Coordinates

A ditrigon with edge lengths a and b has the vertex coordinates

• $\left(\pm\frac{b}{2},\,\frac{2a+b}{2\sqrt{3}}\right)$,

• $\left(\pm\frac{a+b}{2},\,\frac{b-a}{2\sqrt{3}}\right)$,

• $\left(\pm\frac{a}{2},\,\frac{-a-2b}{2\sqrt{3}}\right)$.

For retrograde ditrigons (i.e. Tripods and Propeller tripods), a is negative.

In vertex figures

The ditrigon appears as a vertex figure in one uniform polyhedron, namely the small ditrigonary icosidodecahedron. This ditrigon has edge lengths of 1 and (√5–1)/2.

External links

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

• Klitzing, Richard. "Polygons"