# Ditrigon

Ditrigon Rank2
TypeSemi-uniform
SpaceSpherical
Notation
Bowers style acronymDit
Coxeter diagramx3y
Elements
Edges3+3
Vertices6
Measures (edge lengths a, b)
Circumradius$\sqrt{\frac{a^2+ab+b^2}{3}}$ Area$\frac{\sqrt3}{4}(a^2+4ab+b^2)$ Angle120°
Central density1
Related polytopes
ArmyDit
DualTriambus
ConjugateDitrigon
Abstract properties
Flag count6+6
Net count1
Euler characteristic0
Topological properties
OrientableYes
Properties
SymmetryA2, order 6
ConvexYes
NatureTame

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.