Cubic symmetry

Octahedral symmetry, also known as cubic symmetry and notated B3 or BC3, is a 3D spherical Coxeter group. It is the symmetry group of the cube and octahedron.

Subgroups

 * BC3+ (maximal)
 * A3 (maximal)
 * A3+×2 (maximal)
 * A3+ (maximal)
 * (G2×A1)/2 (maximal)
 * (G2+×A1)/2
 * BC2×A1 (maximal)
 * (BC2×A1)/2
 * (BC2×A1)+
 * BC2×I
 * BC2+×A1
 * (BC2+×A1)/2
 * BC2+×I
 * (A2×A1)+
 * A2×I
 * A2+×I
 * K3
 * K3+
 * K2×I
 * K2+×A1
 * K2+×I
 * ±(I×I×I)
 * A1×I×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)
 * Great rhombicuboctahedron (isogonal)/Disdyakis dodecahedron (isotopic)