# Ditrigon

Ditrigon
Rank2
TypeSemi-uniform
Notation
Bowers style acronymDit
Coxeter diagramx3y
Elements
Edges3+3
Vertices6
Measures (edge lengths a, b)
Circumradius${\displaystyle {\sqrt {\frac {a^{2}+ab+b^{2}}{3}}}}$
Area${\displaystyle {\frac {\sqrt {3}}{4}}(a^{2}+4ab+b^{2})}$
Angle120°
Central density1
Related polytopes
ArmyDit
DualTriambus
ConjugateDitrigon
Abstract & topological properties
Flag count12
Euler characteristic0
OrientableYes
Properties
SymmetryA2, order 6
Flag orbits2
ConvexYes
Net count1
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

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

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 ${\displaystyle {\frac {{\sqrt {5}}-1}{2}}}$.