Hexagonal symmetry

Hexagonal symmetry, also known as higgic symmetry and notated as G₂, is a 2D spherical Coxeter group. It is the symmetry group of the hexagon, with 6 rotation and 6 reflection elements.

Hexagonal symmetry
File:Hexagon with symmetry axes.svg
Rank	2
Space	Spherical
Order	12
Info
Coxeter diagram
Elements
Axes	6 × A1
Related polytopes
Omnitruncate	Dihexagon

Subgroups

• Chiral hexagonal symmetry (maximal)
• Triangular symmetry (maximal)
• Chiral triangular symmetry
• Rectangular symmetry (maximal)
• Inversion symmetry
• Reflection symmetry
• Identity symmetry

Convex polytopes with G₂ symmetry

• Hexagon (regular)
• Dihexagon (isogonal)/Hexambus (isotopic)