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

 * Chiral tetrahedral symmetry (maximal)
 * Chiral square prismatic symmetry (maximal)
 * Chiral square pyramidal symmetry
 * Chiral triangular prismatic symmetry (maximal)
 * Chiral triangular pyramidal symmetry
 * Chiral digonal prismatic symmetry
 * Chiral digonal pyramidal symmetry
 * Identity symmetry

Convex polytopes with B3+ 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)