# Dihexagon

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

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.

## 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.