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.

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)