Dihexagon

Dihexagon
Rank	2
Type	Semi-uniform
Notation
Bowers style acronym	Dihig
Coxeter diagram	x6y
Elements
Edges	6+6
Vertices	12
Vertex figure	Dyad
Measures (edge lengths a, b)
Circumradius	${\sqrt {a^{2}+b^{2}+ab{\sqrt {3}}}}$
Area	${\frac {3{\sqrt {3}}}{2}}(a^{2}+b^{2})+6ab$
Angle	150°
Central density	1
Related polytopes
Army	Dihig
Dual	Hexambus
Abstract & topological properties
Euler characteristic	0
Orientable	Yes
Properties
Symmetry	G2, order 12
Convex	Yes
Nature	Tame

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

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

For retrograde dihexagons, a is negative.