Hexagonal prismatic symmetry

Hexagonal prismatic symmetry
Rank	3
Space	Spherical
Order	24
Info
Coxeter diagram
Elements
Axes	1 × G2×A1, 6 × K2×I
Related polytopes
Omnitruncate	Dihexagonal prism

Hexagonal prismatic symmetry, also known as hippic symmetry and notated as G₂×A₁, is a 3D spherical Coxeter group. It is the symmetry group of the hexagonal prism.

Subgroups

• (G₂×A₁)/2
• (G₂×A₁)+
• G₂×I
• (G₂+×A₁)/2
• G₂+×A₁
• G₂+×I
• A₂×A₁
• (A₂×A₁)+
• A₂×I
• A₂+×A₁
• A₂+×I
• K₃
• K₃+
• K₂×I
• K₂+×A₁
• K₂+×I
• ±(I×I×I)
• A₁×I×I
• I×I×I

Convex polytopes with G₂×A₁ symmetry

• Hexagonal prism (isogonal)/Hexagonal tegum (isotopic)
• Dihexagonal prism (isogonal)/Hexambic tegum (isotopic)