Cubic symmetry

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

Subgroups

 * BC3+
 * A3
 * A3+×2
 * A3+
 * G2×A1/2
 * G2+×A1/2
 * BC2×A1
 * BC2×A1/2
 * BC2×A1+
 * BC2×I
 * BC2+×A1
 * BC2+×A1/2
 * BC2+×I
 * A2×A1+
 * A2×I
 * A2+×I
 * A1×A1×A1
 * A1×A1×A1+
 * A1×A1×I
 * A1×A1+×A1
 * A1×A1+×I
 * A1×A1+×A1/2
 * 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)