Chiral cubic symmetry

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

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.

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)