Chiral cubic symmetry

Chiral cubic symmetry, also known as chiral octahedral symmetry, kicubic symmetry, or notated as B₃+ or BC₃+, is a 3D spherical symmetry group. It is the symmetry group of the snub cube, or equivalently the symmetry group of the cube or octahedron with all the reflections removed.

Chiral cubic symmetry
Rank	3
Space	Spherical
Order	24
Info
Coxeter diagram
Elements
Axes	3 × (BC2×A1)+, 4 × (A2)+, 6 × K3+

Subgroups

• A₃+ (maximal)
• (B₂×A₁)+ (maximal)
• B₂+×I
• (A₂×A₁)+ (maximal)
• A₂+×I
• K₃+
• K₂+×I
• I×I×I

Convex polytopes with BC₃+ symmetry

• Cube (regular)/Octahedron (regular)
• Cuboctahedron (isogonal)/Rhombic dodecahedron (isotopic)
• Truncated cube (isogonal)/Triakis octahedron (isotopic)
• Truncated octahedron (isogonal)/Tetrakis hexahedron (isotopic)
• Small rhombicuboctahedron (isogonal)/Deltoidal icositetrahedron (isotopic)
• Snub cube (isogonal)/Pentagonal icositetrahedron (isotopic)