Square prismatic symmetry

Square prismatic symmetry
Rank	3
Space	Spherical
Order	16
Info
Coxeter diagram
Elements
Axes	1 × BC2×A1, 4 × K2×I
Related polytopes
Omnitruncate	Ditetragonal prism

Square prismatic symmetry, also known as squippic symmetry and notated B₂×A₁ or BC₂×A₁, is a 3D spherical Coxeter group. It is the symmetry group of the square prism and is a subgroup of octahedral symmetry.

Subgroups

• (B₂×A₁)/2 (maximal)
• (B₂×A₁)+ (maximal)
• B₂×I (maximal)
• (B₂+×A₁)/2
• B₂+×A₁ (maximal)
• B₂+×I
• K₃ (maximal)
• K₃+
• K₂×I
• K₂+×A₁
• K₂+×I
• ±(I×I×I)
• A₁×I×I
• I×I×I

Convex polytopes with B₂×A₁ symmetry

• Square prism (isogonal)/Square tegum (isotopic)
• Ditetragonal prism (isogonal)/Tetrambic tegum (isotopic)