# Dihexagon

The dihexagon is a convex semi-uniform dodecagon. As such it has 12 sides that alternate between two edge lengths, with each vertex joining one side of each length. All interior angles of a dihexagon measure 150°. If the side lengths are equal, the result is the regular dodecagon.

Dihexagon
Rank2
TypeSemi-uniform
SpaceSpherical
Notation
Bowers style acronymDihig
Coxeter diagramx6y
Elements
Edges6+6
Vertices12
Measures (edge lengths a, b)
Circumradius${\displaystyle \sqrt{a^2+b^2+ab\sqrt3}}$
Area${\displaystyle \frac{3\sqrt3}{2}(a^2+b^2)+6ab}$
Angle150°
Central density1
Related polytopes
ArmyDihig
DualHexambus
Abstract & topological properties
Euler characteristic0
OrientableYes
Properties
SymmetryG2, order 12
ConvexYes
NatureTame

## Vertex Coordinates

The vertex coordinates of a dihexagon with side lengths a and b are given by

• ${\displaystyle \biggl(\pm\frac{a}{2},\pm\biggl({\frac{a\sqrt{3}}{2}}+b\biggr)\biggr)}$
• ${\displaystyle \biggl(\pm\frac{a+b\sqrt{3}}{2},\pm\frac{a\sqrt{3}+b}{2}\biggr)}$
• ${\displaystyle \biggl(\pm\biggl(a+\frac{b\sqrt{3}}{2}\biggr),\pm\frac{b}{2}\biggr)}$

For retrograde dihexagons, a is negative.